{"id":6548,"date":"2025-08-05T08:44:56","date_gmt":"2025-08-05T08:44:56","guid":{"rendered":"https:\/\/tutorschool.in\/?p=6548"},"modified":"2025-08-07T11:23:46","modified_gmt":"2025-08-07T11:23:46","slug":"class-10-maths-ncert-chapter-1-real-numbers-solutions","status":"publish","type":"post","link":"https:\/\/tutorschool.in\/blog\/class-10-maths-ncert-chapter-1-real-numbers-solutions\/","title":{"rendered":"Class 10 Maths NCERT Chapter 1 (Real Numbers) Solutions"},"content":{"rendered":"<h2>Summary (What we have discussed)<\/h2>\n<p>Hello! Are you using the NCERT textbook to study Class 10 Maths Chapter 1: &#8220;<strong>Real Numbers<\/strong>&#8220;? The <strong>Fundamental Theorem of Arithmetic<\/strong>, <strong>Euclid&#8217;s Division Lemma<\/strong>, and the distinction between <strong>rational and irrational numbers<\/strong> are just a few of the fascinating questions that are covered in this page.<\/p>\n<p>During your studies, you will discover things such as:<\/p>\n<ul>\n<li>How to determine a number&#8217;s <strong>LCM<\/strong> (Least Common Multiple) and <strong>HCF<\/strong> (Highest Common Factor).<\/li>\n<li>How to demonstrate why certain numbers, such as \u221a2 and \u221a3, are <strong>irrational<\/strong>.<\/li>\n<li>How to determine if a <strong>decimal<\/strong> is non-terminating or terminating.<\/li>\n<\/ul>\n<p>\t\t\t\t\t<button id=\"e-n-tab-title-1191938011\" aria-selected=\"true\" data-tab-index=\"1\" role=\"tab\" tabindex=\"0\" aria-controls=\"e-n-tab-content-1191938011\" style=\"--n-tabs-title-order: 1;\"><br \/>\n\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M352 96c0-53.02-42.98-96-96-96s-96 42.98-96 96 42.98 96 96 96 96-42.98 96-96zM233.59 241.1c-59.33-36.32-155.43-46.3-203.79-49.05C13.55 191.13 0 203.51 0 219.14v222.8c0 14.33 11.59 26.28 26.49 27.05 43.66 2.29 131.99 10.68 193.04 41.43 9.37 4.72 20.48-1.71 20.48-11.87V252.56c-.01-4.67-2.32-8.95-6.42-11.46zm248.61-49.05c-48.35 2.74-144.46 12.73-203.78 49.05-4.1 2.51-6.41 6.96-6.41 11.63v245.79c0 10.19 11.14 16.63 20.54 11.9 61.04-30.72 149.32-39.11 192.97-41.4 14.9-.78 26.49-12.73 26.49-27.06V219.14c-.01-15.63-13.56-28.01-29.81-27.09z\"><\/path><\/svg>\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 512 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M352 96c0-53.02-42.98-96-96-96s-96 42.98-96 96 42.98 96 96 96 96-42.98 96-96zM233.59 241.1c-59.33-36.32-155.43-46.3-203.79-49.05C13.55 191.13 0 203.51 0 219.14v222.8c0 14.33 11.59 26.28 26.49 27.05 43.66 2.29 131.99 10.68 193.04 41.43 9.37 4.72 20.48-1.71 20.48-11.87V252.56c-.01-4.67-2.32-8.95-6.42-11.46zm248.61-49.05c-48.35 2.74-144.46 12.73-203.78 49.05-4.1 2.51-6.41 6.96-6.41 11.63v245.79c0 10.19 11.14 16.63 20.54 11.9 61.04-30.72 149.32-39.11 192.97-41.4 14.9-.78 26.49-12.73 26.49-27.06V219.14c-.01-15.63-13.56-28.01-29.81-27.09z\"><\/path><\/svg><br \/>\n\t\t\t\tLong Answer Type Questions<br \/>\n\t\t<\/button><\/p>\n<table>\n<tbody>\n<tr>\n<td>Class 10<\/td>\n<td>MATHS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Chapter<\/td>\n<td>REAL NUMBERS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>NCERT MATHS (ENGLISH)<\/td>\n<td>LONG ANSWER TYPE QUESTIONS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Medium<\/td>\n<td>English<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Academic Year<\/td>\n<td>\n<p>2023-2024<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Question 1<\/strong><\/p>\n<p>For some integer\u00a0m, every even integer is of the form<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques1\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 2<\/strong><\/p>\n<p>For some integer\u00a0q, every odd integer is of the form<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques2\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 3<\/strong><\/p>\n<p>n<sup>2<\/sup>\u22121\u00a0is divisible by\u00a08, if\u00a0n\u00a0is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques3\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 4<\/strong><\/p>\n<p>If HCF of\u00a065\u00a0and\u00a0117\u00a0is expressible in the form\u00a065m\u2212117, then the value of\u00a0m\u00a0is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques4\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 5<\/strong><\/p>\n<p>The largest number which divides\u00a070\u00a0and\u00a0125, leaving remainder\u00a05 and 8\u00a0respectively, is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques5\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 6<\/strong><\/p>\n<p>If two positive integers\u00a0m\u00a0and\u00a0n\u00a0are expressible in the form\u00a0m=pq<sup>3<\/sup>\u00a0and\u00a0n=p<sup>3<\/sup>q<sup>2<\/sup>\u00a0, where\u00a0p,\u00a0q\u00a0are prime numbers, then HCF\u00a0(m,\u00a0n)=<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques6\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 7<\/strong><\/p>\n<p>If two positive integers\u00a0a\u00a0and\u00a0b\u00a0are expressible in the form\u00a0a=pq<sup>2<\/sup>\u00a0and\u00a0b=p<sup>3<\/sup>q\u00a0;\u00a0p,\u00a0q\u00a0being prime numbers, then LCM\u00a0(a,\u00a0b) is\u00a0<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques7\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 8<\/strong><\/p>\n<p>The product of a non-zero rational number with an irrational number is always a\/an<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques8\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 9<\/strong><\/p>\n<p>What is the least number that is divisible by all the numbers\u00a01\u00a0to\u00a010<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques9\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 10<\/strong><\/p>\n<p>The decimal expansion of the rational number\u00a014587\/1250\u00a0will terminate after<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques10\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 11<\/strong><\/p>\n<p>Write whether every positive integer can be of the form\u00a04q+2\u00a0where q is an integer, Justify your answer<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques11\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 12<\/strong><\/p>\n<p>The product of two consecutive integers is divisible by 2. Is this statement true or false. Give Reason?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques12\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 13<\/strong><\/p>\n<p>The product of any three consecutive natural numbers is divisible by 6 (True\/false).<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques13\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 14<\/strong><\/p>\n<p>Write whether the square of any positive integer can be of the form 3m+2, where m is a natural number. Justify answer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques14\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 15<\/strong><\/p>\n<p>A positive integer is the form of 3q+1 q, being a natural number. Can you write its square in any form other than 3m+1 i.e. 3m or 3m+2 for some integer? Justify your answer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques15\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 16<\/strong><\/p>\n<p>The number 525 and 3000 are both divisible only by 3,5,15,25,75. What is HCF (525, 3000)? Justify your answer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques16\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 17<\/strong><\/p>\n<p>Explain why\u00a03\u00d75\u00d77+7\u00a0is a composite number.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques17\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 18<\/strong><\/p>\n<p>Can two number have 18 as their HCF and 380 as their LCM? Give reason<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques18\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 19<\/strong><\/p>\n<p>Without actually performing the long divison, find if\u00a0987\/10500\u00a0will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques19\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 20<\/strong><\/p>\n<p>A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the from\u00a0p\/q\u00a0? Give reason<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques20\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 21<\/strong><\/p>\n<p>Prove that the square of any positive integer is of the form\u00a04q\u00a0or\u00a04q+1\u00a0for some integer\u00a0q\u00a0.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques21\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 22<\/strong><\/p>\n<p>Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3, for some integer m.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques22\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 23<\/strong><\/p>\n<p>Show that the square of any positive integer cannot be of the form 5q+2 or 5q+3 for some integer q.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques23\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 24<\/strong><\/p>\n<p>Show that the square of any positive integer cannot be of the form 6m+2 or 6m+5 for some integer q.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques24\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 25<\/strong><\/p>\n<p>Show that the square of any odd integer is of the form 4m+1, for some integer m.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques25\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 26<\/strong><\/p>\n<p>If n is an odd positive integer, show that\u00a0(n<sup>2<\/sup>\u22121)\u00a0is divisible by 8.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques26\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 27<\/strong><\/p>\n<p>Prove that if\u00a0x and y\u00a0are odd positive integers, then\u00a0x<sup>2<\/sup>+y<sup>2<\/sup>\u00a0is even but not divisible by 4.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques27\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 28<\/strong><\/p>\n<p>Use Euclid division algorithm to find the HCF of 441, 567 and 693.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques28\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 29<\/strong><\/p>\n<p>Using Euclid&#8217;s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques29\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 30<\/strong><\/p>\n<p>Prove that\u00a0\u221a3+\u221a5\u00a0is irrational<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques30\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 31<\/strong><\/p>\n<p>Show that\u00a012<sup>n<\/sup>\u00a0cannot end with the digits\u00a00\u00a0or\u00a05\u00a0for any natural number\u00a0n<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques31\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 32<\/strong><\/p>\n<p>In a morning walk, three persons step off together and their steps measure\u00a040cm,42cm and 45cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques32\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 33<\/strong><\/p>\n<p>Write the denominator of the rational number\u00a0257\/5000\u00a0in the form\u00a02<sup>m<\/sup>\u00d75<sup>n<\/sup>, where m, n and non-negative integers. Hence, write its decimal expansion without actual division.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques33\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 34<\/strong><\/p>\n<p>Prove that\u00a0\u221ap+\u221aq\u00a0is an irrational, where\u00a0pandq\u00a0are primes.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques34\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 35<\/strong><\/p>\n<p>Show that the cube of a positive integer of the form\u00a06q+r,q\u00a0is an integer and r=0,1,2,3,4,5 is also of the form 6m+r<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-class-10-chapter-1real-numbers-ques-35-solution\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 36<\/strong><\/p>\n<p>Show that one and only one out of\u00a0n,n+2or,n+4\u00a0is divisible by 3, where\u00a0n\u00a0is any positive integer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques36\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 37<\/strong><\/p>\n<p>Prove that one of every three consecutive positive integers is divisible by 3.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques37\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 38<\/strong><\/p>\n<p>For any positive integer\u00a0n\u00a0, prove that\u00a0n<sup>3<\/sup>\u2212n\u00a0is divisible by 6.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques38\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 39<\/strong><\/p>\n<p>Show that one and only one out of\u00a0n,n+4,n+8,n+12andn+16\u00a0is divisible by 5, where n is any positive integer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques39\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<table>\n<tbody>\n<tr>\n<td>Class 10<\/td>\n<td>MATHS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Chapter<\/td>\n<td>REAL NUMBERS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>NCERT MATHS (ENGLISH)<\/td>\n<td>LONG ANSWER TYPE QUESTIONS<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Medium<\/td>\n<td>English<\/td>\n<\/tr>\n<\/tbody>\n<tbody>\n<tr>\n<td>Academic Year<\/td>\n<td>\n<p>2023-2024<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p><strong>Question 1<\/strong><\/p>\n<p>For some integer\u00a0m, every even integer is of the form<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques1\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 2<\/strong><\/p>\n<p>For some integer\u00a0q, every odd integer is of the form<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques2\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 3<\/strong><\/p>\n<p>n<sup>2<\/sup>\u22121\u00a0is divisible by\u00a08, if\u00a0n\u00a0is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques3\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 4<\/strong><\/p>\n<p>If HCF of\u00a065\u00a0and\u00a0117\u00a0is expressible in the form\u00a065m\u2212117, then the value of\u00a0m\u00a0is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques4\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 5<\/strong><\/p>\n<p>The largest number which divides\u00a070\u00a0and\u00a0125, leaving remainder\u00a05 and 8\u00a0respectively, is<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques5\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 6<\/strong><\/p>\n<p>If two positive integers\u00a0m\u00a0and\u00a0n\u00a0are expressible in the form\u00a0m=pq<sup>3<\/sup>\u00a0and\u00a0n=p<sup>3<\/sup>q<sup>2<\/sup>\u00a0, where\u00a0p,\u00a0q\u00a0are prime numbers, then HCF\u00a0(m,\u00a0n)=<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques6\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 7<\/strong><\/p>\n<p>If two positive integers\u00a0a\u00a0and\u00a0b\u00a0are expressible in the form\u00a0a=pq<sup>2<\/sup>\u00a0and\u00a0b=p<sup>3<\/sup>q\u00a0;\u00a0p,\u00a0q\u00a0being prime numbers, then LCM\u00a0(a,\u00a0b) is\u00a0<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques7\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 8<\/strong><\/p>\n<p>The product of a non-zero rational number with an irrational number is always a\/an<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques8\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 9<\/strong><\/p>\n<p>What is the least number that is divisible by all the numbers\u00a01\u00a0to\u00a010<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques9\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 10<\/strong><\/p>\n<p>The decimal expansion of the rational number\u00a014587\/1250\u00a0will terminate after<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques10\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 11<\/strong><\/p>\n<p>Write whether every positive integer can be of the form\u00a04q+2\u00a0where q is an integer, Justify your answer<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques11\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 12<\/strong><\/p>\n<p>The product of two consecutive integers is divisible by 2. Is this statement true or false. Give Reason?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques12\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 13<\/strong><\/p>\n<p>The product of any three consecutive natural numbers is divisible by 6 (True\/false).<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques13\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 14<\/strong><\/p>\n<p>Write whether the square of any positive integer can be of the form 3m+2, where m is a natural number. Justify answer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques14\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 15<\/strong><\/p>\n<p>A positive integer is the form of 3q+1 q, being a natural number. Can you write its square in any form other than 3m+1 i.e. 3m or 3m+2 for some integer? Justify your answer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques15\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 16<\/strong><\/p>\n<p>The number 525 and 3000 are both divisible only by 3,5,15,25,75. What is HCF (525, 3000)? Justify your answer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques16\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 17<\/strong><\/p>\n<p>Explain why\u00a03\u00d75\u00d77+7\u00a0is a composite number.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques17\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 18<\/strong><\/p>\n<p>Can two number have 18 as their HCF and 380 as their LCM? Give reason<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques18\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 19<\/strong><\/p>\n<p>Without actually performing the long divison, find if\u00a0987\/10500\u00a0will have terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques19\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 20<\/strong><\/p>\n<p>A rational number in its decimal expansion is 327.7081. What can you say about the prime factors of q, when this number is expressed in the from\u00a0p\/q\u00a0? Give reason<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques20\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 21<\/strong><\/p>\n<p>Prove that the square of any positive integer is of the form\u00a04q\u00a0or\u00a04q+1\u00a0for some integer\u00a0q\u00a0.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques21\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 22<\/strong><\/p>\n<p>Show that cube of any positive integer is of the form 4m, 4m+1 or 4m+3, for some integer m.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques22\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 23<\/strong><\/p>\n<p>Show that the square of any positive integer cannot be of the form 5q+2 or 5q+3 for some integer q.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques23\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 24<\/strong><\/p>\n<p>Show that the square of any positive integer cannot be of the form 6m+2 or 6m+5 for some integer q.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques24\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 25<\/strong><\/p>\n<p>Show that the square of any odd integer is of the form 4m+1, for some integer m.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques25\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 26<\/strong><\/p>\n<p>If n is an odd positive integer, show that\u00a0(n<sup>2<\/sup>\u22121)\u00a0is divisible by 8.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques26\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 27<\/strong><\/p>\n<p>Prove that if\u00a0x and y\u00a0are odd positive integers, then\u00a0x<sup>2<\/sup>+y<sup>2<\/sup>\u00a0is even but not divisible by 4.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques27\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 28<\/strong><\/p>\n<p>Use Euclid division algorithm to find the HCF of 441, 567 and 693.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques28\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 29<\/strong><\/p>\n<p>Using Euclid&#8217;s division algorithm, find the largest number that divides 1251, 9377 and 15628 leaving remainders 1, 2 and 3, respectively.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques29\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 30<\/strong><\/p>\n<p>Prove that\u00a0\u221a3+\u221a5\u00a0is irrational<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques30\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 31<\/strong><\/p>\n<p>Show that\u00a012<sup>n<\/sup>\u00a0cannot end with the digits\u00a00\u00a0or\u00a05\u00a0for any natural number\u00a0n<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques31\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 32<\/strong><\/p>\n<p>In a morning walk, three persons step off together and their steps measure\u00a040cm,42cm and 45cm, respectively. What is the minimum distance each should walk so that each can cover the same distance in complete steps?<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques32\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 33<\/strong><\/p>\n<p>Write the denominator of the rational number\u00a0257\/5000\u00a0in the form\u00a02<sup>m<\/sup>\u00d75<sup>n<\/sup>, where m, n and non-negative integers. Hence, write its decimal expansion without actual division.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques33\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 34<\/strong><\/p>\n<p>Prove that\u00a0\u221ap+\u221aq\u00a0is an irrational, where\u00a0pandq\u00a0are primes.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques34\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 35<\/strong><\/p>\n<p>Show that the cube of a positive integer of the form\u00a06q+r,q\u00a0is an integer and r=0,1,2,3,4,5 is also of the form 6m+r<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-class-10-chapter-1real-numbers-ques-35-solution\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 36<\/strong><\/p>\n<p>Show that one and only one out of\u00a0n,n+2or,n+4\u00a0is divisible by 3, where\u00a0n\u00a0is any positive integer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques36\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 37<\/strong><\/p>\n<p>Prove that one of every three consecutive positive integers is divisible by 3.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques37\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 38<\/strong><\/p>\n<p>For any positive integer\u00a0n\u00a0, prove that\u00a0n<sup>3<\/sup>\u2212n\u00a0is divisible by 6.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques38\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n<p><strong>Question 39<\/strong><\/p>\n<p>Show that one and only one out of\u00a0n,n+4,n+8,n+12andn+16\u00a0is divisible by 5, where n is any positive integer.<\/p>\n<p>\t\t\t\t\t<a href=\"https:\/\/tutorschool.in\/ncert-sol-class10-real-numbers-ques39\/\"><br \/>\n\t\t\t\t<svg aria-hidden=\"true\" viewBox=\"0 0 576 512\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\"><path d=\"M288 144a110.94 110.94 0 0 0-31.24 5 55.4 55.4 0 0 1 7.24 27 56 56 0 0 1-56 56 55.4 55.4 0 0 1-27-7.24A111.71 111.71 0 1 0 288 144zm284.52 97.4C518.29 135.59 410.93 64 288 64S57.68 135.64 3.48 241.41a32.35 32.35 0 0 0 0 29.19C57.71 376.41 165.07 448 288 448s230.32-71.64 284.52-177.41a32.35 32.35 0 0 0 0-29.19zM288 400c-98.65 0-189.09-55-237.93-144C98.91 167 189.34 112 288 112s189.09 55 237.93 144C477.1 345 386.66 400 288 400z\"><\/path><\/svg><br \/>\n\t\t\t\t\t\t\t\t\tView Solution<br \/>\n\t\t\t\t\t<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Summary (What we have discussed) Hello! Are you using the NCERT textbook to study Class 10 Maths Chapter 1: &#8220;Real Numbers&#8220;? The Fundamental Theorem of Arithmetic, Euclid&#8217;s Division Lemma, and the distinction between rational and irrational numbers are just a few of the fascinating questions that are covered in this page. During your studies, you [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":7093,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[12,74],"tags":[],"class_list":["post-6548","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-education","category-maths"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.7 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Class 10 Maths NCERT Chapter 1 (Real Numbers) Solutions<\/title>\n<meta name=\"description\" content=\"Finding Class 10 Maths NCERT Chapter 1 (Real Numbers) Solutions ? 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