{"id":4985,"date":"2016-05-19T11:49:00","date_gmt":"2016-05-19T06:19:00","guid":{"rendered":"http:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/"},"modified":"2018-06-16T17:36:43","modified_gmt":"2018-06-16T12:06:43","slug":"ncert-solutions-class-9-maths-exercise-1-5","status":"publish","type":"post","link":"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/","title":{"rendered":"NCERT Solutions for Class 9 Maths Exercise 1.5"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_76 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\" style=\"cursor:inherit\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"Toggle Table of Content\"><span class=\"ez-toc-js-icon-con\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/span><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-toggle-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#NCERT_Solutions_for_Class_9_Maths_Number_Systems\" >NCERT Solutions for Class 9 Maths Number Systems<\/a><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><ul class='ez-toc-list-level-6' ><li class='ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#1_Classify_the_following_numbers_as_rational_or_irrational\" >1. Classify the following numbers as rational or irrational:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#Therefore_we_conclude_thatis_a_rational_number\" >Therefore, we conclude thatis a rational number.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#2_Simplify_each_of_the_following_expressions\" >2. Simplify each of the following expressions:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#Therefore_on_simplifying_we_get\" >Therefore, on simplifying, we get.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#3_Recall_is_defined_as_the_ratio_of_the_circumference_say_c_of_a_circle_to_its_diameter_say_d_That_is_This_seems_to_contradict_the_fact_that_is_irrational_How_will_you_resolve_this_contradiction\" >3. Recall, is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is,. This seems to contradict the fact that is irrational. How will you resolve this contradiction?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#4_Represent_93_on_the_number_line\" >4. Represent 9.3 on the number line.<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#5_Rationalize_the_denominators_of_the_following\" >5. Rationalize the denominators of the following:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#We_need_to_multiply_the_numerator_and_denominator_ofby_to_get\" >We need to multiply the numerator and denominator ofby, to get<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#We_need_to_apply_the_formulain_the_denominator_to_get\" >We need to apply the formulain the denominator to get<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-6'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#We_need_to_apply_the_formulain_the_denominator_to_get-2\" >We need to apply the formulain the denominator to get<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#NCERT_Solutions_for_Class_9_Maths_Exercise_15\" >NCERT Solutions for Class 9 Maths Exercise 1.5<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/#CBSE_app_for_Class_9\" >CBSE app for Class 9<\/a><\/li><\/ul><\/nav><\/div>\n<p>NCERT Solutions for Class 9 Maths Exercise 1.5 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter wise NCERT solution for Maths Book for all the chapters can be downloaded from our website and myCBSEguide mobile app for free.<\/p>\n<p style=\"text-align: center;\"><strong>NCERT solutions for Class 9 Maths\u00a0Number Systems\u00a0<a class=\"button\" href=\"https:\/\/mycbseguide.com\/downloads\/cbse-class-09-mathematics-number-systems\/1235\/ncert-solutions\/5\/\">Download as PDF<\/a><\/strong><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/media-mycbseguide.s3.ap-south-1.amazonaws.com\/images\/blog\/09_Class_Maths_Book.jpg\" alt=\"NCERT Solutions for Class 9 Maths Exercise 1.5\" width=\"159\" height=\"204\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Number_Systems\"><\/span>NCERT Solutions for Class 9 Maths Number Systems<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"1_Classify_the_following_numbers_as_rational_or_irrational\"><\/span><strong>1. Classify the following numbers as rational or irrational:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 24px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image001.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 32px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image002.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 48px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image003.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv) <img decoding=\"async\" style=\"height: 44px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image004.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(v) <img decoding=\"async\" style=\"height: 19px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image005.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(i)<\/strong> <img decoding=\"async\" style=\"height: 24px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image001.png\" \/><\/p>\n<p style=\"text-align: justify;\">We know that<img decoding=\"async\" style=\"height: 25px; width: 293px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image006.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 137px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image007.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 21px; width: 83px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image008.png\" \/><\/p>\n<p style=\"text-align: justify;\">which is also an irrational number.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 24px; width: 47px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image001.png\" \/>is an irrational number.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 32px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image002.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 32px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image002.png\" \/><img decoding=\"async\" style=\"height: 24px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image009.png\" \/><\/p>\n<p style=\"text-align: justify;\">= 3<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Therefore_we_conclude_thatis_a_rational_number\"><\/span>Therefore, we conclude that<img decoding=\"async\" style=\"height: 32px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image002.png\" \/>is a rational number.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> <img decoding=\"async\" style=\"height: 48px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image003.png\" \/><\/p>\n<p style=\"text-align: justify;\">We can cancel<img decoding=\"async\" style=\"height: 24px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image010.png\" \/>in the numerator and denominator, as<img decoding=\"async\" style=\"height: 24px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image010.png\" \/>is the common number in numerator as well as denominator, to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 48px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image011.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 48px; width: 36px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image003.png\" \/>is a rational number.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> <img decoding=\"async\" style=\"height: 44px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image004.png\" \/><\/p>\n<p style=\"text-align: justify;\">We know that<img decoding=\"async\" style=\"height: 25px; width: 285px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image012.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">We can conclude that, when 1 is divided by<img decoding=\"async\" style=\"height: 23px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image013.png\" \/>, we will get an irrational number.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 44px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image004.png\" \/>is an irrational number.<\/p>\n<p style=\"text-align: justify;\"><strong>(v) <\/strong><img decoding=\"async\" style=\"height: 19px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image005.png\" \/><\/p>\n<p style=\"text-align: justify;\">We know that<img decoding=\"async\" style=\"height: 21px; width: 292px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image014.png\" \/><\/p>\n<p style=\"text-align: justify;\">We can conclude that<img decoding=\"async\" style=\"height: 19px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image005.png\" \/>will also be an irrational number.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that<img decoding=\"async\" style=\"height: 19px; width: 24px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image005.png\" \/>is an irrational number.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"2_Simplify_each_of_the_following_expressions\"><\/span><strong>2. Simplify each of the following expressions:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 32px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image015.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii) <img decoding=\"async\" style=\"height: 32px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image016.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii) <img decoding=\"async\" style=\"height: 36px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image017.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<img decoding=\"async\" style=\"height: 32px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image018.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> <img decoding=\"async\" style=\"height: 32px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image015.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to apply distributive law to find value of<img decoding=\"async\" style=\"height: 32px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image015.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 32px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image015.png\" \/><img decoding=\"async\" style=\"height: 32px; width: 171px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image019.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 143px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image020.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"Therefore_on_simplifying_we_get\"><\/span>Therefore, on simplifying<img decoding=\"async\" style=\"height: 32px; width: 115px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image015.png\" \/>, we get<img decoding=\"async\" style=\"height: 24px; width: 131px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image021.png\" \/>.<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 32px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image016.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to apply distributive law to find value of<img decoding=\"async\" style=\"height: 32px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image016.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 32px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image016.png\" \/><img decoding=\"async\" style=\"height: 32px; width: 167px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image022.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 127px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image023.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, on simplifying<img decoding=\"async\" style=\"height: 32px; width: 112px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image016.png\" \/>, we get 6.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> <img decoding=\"async\" style=\"height: 36px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image017.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to apply the formula<img decoding=\"async\" style=\"height: 29px; width: 152px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image024.png\" \/> to find value of<img decoding=\"async\" style=\"height: 36px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image017.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 36px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image017.png\" \/><img decoding=\"async\" style=\"height: 36px; width: 195px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image025.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 96px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image026.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 77px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image027.png\" \/><\/p>\n<p style=\"text-align: justify;\">=6<\/p>\n<p style=\"text-align: justify;\">Therefore, on simplifying<img decoding=\"async\" style=\"height: 36px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image017.png\" \/>, we get<img decoding=\"async\" style=\"height: 24px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image028.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> <img decoding=\"async\" style=\"height: 32px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image029.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to apply the formula<img decoding=\"async\" style=\"height: 27px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image030.png\" \/> to find value of<img decoding=\"async\" style=\"height: 36px; width: 76px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image017.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 32px; width: 138px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image031.png\" \/><img decoding=\"async\" style=\"height: 36px; width: 108px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image032.png\" \/><\/p>\n<p style=\"text-align: justify;\">= 5-2<\/p>\n<p style=\"text-align: justify;\">=3<\/p>\n<p style=\"text-align: justify;\">Therefore, on simplifying<img decoding=\"async\" style=\"height: 32px; width: 139px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image029.png\" \/>, we get 3.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"3_Recall_is_defined_as_the_ratio_of_the_circumference_say_c_of_a_circle_to_its_diameter_say_d_That_is_This_seems_to_contradict_the_fact_that_is_irrational_How_will_you_resolve_this_contradiction\"><\/span><strong>3. Recall, <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image033.png\" \/>is defined as the ratio of the circumference (say <em>c<\/em>) of a circle to its diameter (say <em>d<\/em>). That is,<img decoding=\"async\" style=\"height: 41px; width: 44px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image034.png\" \/>. This seems to contradict the fact that <img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image033.png\" \/>is irrational. How will you resolve this contradiction?<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>We know that when we measure the length of a line or a figure by using a scale or any device, we do not get an exact measurement. In fact, we get an approximate rational value. So, we are not able to realize that either circumference (<em>c<\/em>) or diameter(<em>d<\/em>) of a circle is irrational.<\/p>\n<p style=\"text-align: justify;\">Therefore, we can conclude that as such there is not any contradiction regarding the value of<img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image033.png\" \/> and we realize that the value of<img decoding=\"async\" style=\"height: 15px; width: 15px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image033.png\" \/>is irrational.<\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"4_Represent_93_on_the_number_line\"><\/span><strong>4. Represent 9<em>.<\/em>3 on the number line.<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>Ans. <\/strong>Mark the distance 9.3 units from a fixed point A on a given line to obtain a point B such that AB = 9.3 units. From B mark a distance of 1 unit and call the new point as C. Find the mid-point of AC and call that point as O. Draw a semi-circle with centre O and radius OC = 5.15 units. Draw a line perpendicular to AC passing through B cutting the semi-circle at D. Then BD = <img decoding=\"async\" style=\"height: 24px; width: 39px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image035.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 164px; width: 324px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image036.png\" \/><\/p>\n<hr \/>\n<p style=\"text-align: center;\">NCERT Solutions for Class 9 Maths Exercise 1.5<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"5_Rationalize_the_denominators_of_the_following\"><\/span><strong>5. Rationalize the denominators of the following:<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><strong>(i) <img decoding=\"async\" style=\"height: 44px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image037.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image038.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image039.png\" \/> <\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<img decoding=\"async\" style=\"height: 44px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image040.png\" \/><\/strong><\/p>\n<p style=\"text-align: justify;\"><strong>Ans. (i)<\/strong> <img decoding=\"async\" style=\"height: 44px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image037.png\" \/><\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"We_need_to_multiply_the_numerator_and_denominator_ofby_to_get\"><\/span>We need to multiply the numerator and denominator of<img decoding=\"async\" style=\"height: 44px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image037.png\" \/>by<img decoding=\"async\" style=\"height: 24px; width: 25px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image010.png\" \/>, to get<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 48px; width: 101px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image041.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that on rationalizing the denominator of<img decoding=\"async\" style=\"height: 44px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image037.png\" \/>, we get<img decoding=\"async\" style=\"height: 45px; width: 28px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image042.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong>(ii)<\/strong> <img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image038.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to multiply the numerator and denominator of<img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image038.png\" \/>by<img decoding=\"async\" style=\"height: 24px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image043.png\" \/>, to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 57px; width: 284px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image044.png\" \/>.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"We_need_to_apply_the_formulain_the_denominator_to_get\"><\/span>We need to apply the formula<img decoding=\"async\" style=\"height: 27px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image030.png\" \/>in the denominator to get<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 60px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image045.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 45px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image046.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 24px; width: 75px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image047.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that on rationalizing the denominator of<img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image038.png\" \/>, we get<img decoding=\"async\" style=\"height: 24px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image043.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong>(iii)<\/strong> <img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image039.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to multiply the numerator and denominator of<img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image039.png\" \/>by<img decoding=\"async\" style=\"height: 24px; width: 59px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image048.png\" \/>, to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 57px; width: 283px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image049.png\" \/>.<\/p>\n<h6 style=\"text-align: justify;\"><span class=\"ez-toc-section\" id=\"We_need_to_apply_the_formulain_the_denominator_to_get-2\"><\/span>We need to apply the formula<img decoding=\"async\" style=\"height: 27px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image030.png\" \/>in the denominator to get<span class=\"ez-toc-section-end\"><\/span><\/h6>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 60px; width: 172px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image050.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 45px; width: 73px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image051.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 45px; width: 81px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image052.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that on rationalizing the denominator of<img decoding=\"async\" style=\"height: 44px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image039.png\" \/>, we get<img decoding=\"async\" style=\"height: 45px; width: 61px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image053.png\" \/>.<\/p>\n<p style=\"text-align: justify;\"><strong>(iv)<\/strong> <img decoding=\"async\" style=\"height: 44px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image040.png\" \/><\/p>\n<p style=\"text-align: justify;\">We need to multiply the numerator and denominator of<img decoding=\"async\" style=\"height: 44px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image040.png\" \/>by<img decoding=\"async\" style=\"height: 24px; width: 48px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image054.png\" \/>, to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 57px; width: 237px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image055.png\" \/>.<\/p>\n<p style=\"text-align: justify;\">We need to apply the formula<img decoding=\"async\" style=\"height: 27px; width: 151px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image030.png\" \/>in the denominator to get<\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 60px; width: 148px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image056.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 45px; width: 63px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image057.png\" \/><\/p>\n<p style=\"text-align: justify;\"><img decoding=\"async\" style=\"height: 45px; width: 67px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image058.png\" \/><\/p>\n<p style=\"text-align: justify;\">Therefore, we conclude that on rationalizing the denominator of<img decoding=\"async\" style=\"height: 44px; width: 49px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image040.png\" \/>, we get<img decoding=\"async\" style=\"height: 45px; width: 51px;\" src=\"https:\/\/media-mycbseguide.s3.amazonaws.com\/images\/static\/ncert\/09\/maths\/ch01\/Ex1.5\/image059.png\" \/>.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"NCERT_Solutions_for_Class_9_Maths_Exercise_15\"><\/span>NCERT Solutions for Class 9 Maths Exercise 1.5<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>NCERT Solutions Class 9 Maths PDF (Download) Free from myCBSEguide app and myCBSEguide website. Ncert solution class 9 Maths includes text book solutions from Mathematics Book. NCERT Solutions for CBSE Class 9 Maths have total 15 chapters. 9 Maths NCERT Solutions in PDF for free Download on our website. Ncert Maths class 9 solutions PDF and Maths ncert class 9 PDF solutions with latest modifications and as per the latest CBSE syllabus are only available in myCBSEguide.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"CBSE_app_for_Class_9\"><\/span>CBSE app for Class 9<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To download NCERT Solutions for Class 9 Maths, Computer Science, Home Science,Hindi ,English, Social Science do check myCBSEguide app or website. myCBSEguide provides sample papers with solution, test papers for chapter-wise practice, NCERT solutions, NCERT Exemplar solutions, quick revision notes for ready reference, CBSE guess papers and CBSE important question papers. Sample Paper all are made available through\u00a0<a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.techchefs.MyCBSEGuide&amp;referrer=utm_source%3Dmycbse_bottom%26utm_medium%3Dtext%26utm_campaign%3Dmycbseads\"><strong>the best app for CBSE students<\/strong><\/a>\u00a0and myCBSEguide website.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions for Class 9 Maths Exercise 1.5 book solutions are available in PDF format for free download. These ncert book chapter wise questions and answers are very helpful for CBSE board exam. CBSE recommends NCERT books and most of the questions in CBSE exam are asked from NCERT text books. Class 9 Maths chapter &#8230; <a title=\"NCERT Solutions for Class 9 Maths Exercise 1.5\" class=\"read-more\" href=\"https:\/\/mycbseguide.com\/blog\/ncert-solutions-class-9-maths-exercise-1-5\/\" aria-label=\"More on NCERT Solutions for Class 9 Maths Exercise 1.5\">Read more<\/a><\/p>\n","protected":false},"author":1,"featured_media":-1,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1376,281],"tags":[283,1344,321,1485,216],"class_list":["post-4985","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics-cbse-class-09","category-ncert-solutions","tag-cbse-study-material","tag-class-9","tag-mathematics","tag-maths","tag-ncert-solutions"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v26.0 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>NCERT Solutions for Class 9 Maths Exercise 1.5 | myCBSEguide<\/title>\n<meta name=\"description\" content=\"NCERT Solutions for Class 9 Maths Exercise 1.5 in PDF format for free download. 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