{"id":4025,"date":"2023-02-01T06:54:29","date_gmt":"2023-02-01T06:54:29","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=4025"},"modified":"2023-02-01T06:54:29","modified_gmt":"2023-02-01T06:54:29","slug":"ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/","title":{"rendered":"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 9 Maths\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 1 (Number Systems )\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">The NCERT Solutions in English Language for Class 9 Mathematics\u00a0<strong>Chapter &#8211; 1 Number Systems\u00a0<\/strong>Exercise 1.5 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>Chapter 1: Number Systems<\/strong><\/span><\/p>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.1<\/a><\/li>\n<li><span style=\"color: #000000;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.2<\/a><\/span><\/li>\n<li><span style=\"color: #000000;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-3\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.3<\/a><\/span><\/li>\n<li><span style=\"color: #000000;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-4\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.4<\/a><\/span><\/li>\n<li><span style=\"color: #000000;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-6\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 9 Maths Ex &#8211; 1.6<\/a><\/span><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 1.5\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Classify the following numbers as rational or irrational:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4209\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"552\" height=\"112\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png 651w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1-300x61.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1-480x97.png 480w\" sizes=\"auto, (max-width: 552px) 100vw, 552px\" \/><br \/>\n<\/strong><strong>Answer &#8211;<br \/>\n<\/strong><strong>(i) 2 \u2013\u221a5<br \/>\n<\/strong>Since, it is a difference of a rational and an irrational number.<br \/>\n\u2234 2 \u2013 \u221a5 is an irrational number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) (3 +\u221a23) &#8211; \u221a23<br \/>\n<\/strong>\u21d2 (3 + <strong>\u221a<\/strong>23) \u2013 \u221a23 = 3 + <strong>\u221a<\/strong>23 \u2013 \u221a23<br \/>\n= 3<br \/>\nwhich is a rational number.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{2\\sqrt{7}}{7\\sqrt{7}}}\" alt=\"\\mathbf{\\frac{2\\sqrt{7}}{7\\sqrt{7}}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2\\sqrt{7}}{7\\sqrt{7}}\" alt=\"\\frac{2\\sqrt{7}}{7\\sqrt{7}}\" align=\"absmiddle\" \/>\u00a0 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{2}{7}\" alt=\"\\frac{2}{7}\" align=\"absmiddle\" \/>, which is a rational number.<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{\\sqrt{2}}}\" alt=\"\\mathbf{\\frac{1}{\\sqrt{2}}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>\u2235 The quotient of rational and irrational number is an irrational number.<br \/>\n\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{\\sqrt{2}}\" alt=\"\\frac{1}{\\sqrt{2}}\" align=\"absmiddle\" \/>\u00a0 is an irrational number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) 2\u03c0<br \/>\n<\/strong>2\u03c0 = 2 x \u03c0<br \/>\n\u2235 Product of a rational and an irrational number is an irrational number.<br \/>\n\u2234 2\u03c0 is an irrational number.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Simplify each of the following expressions:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4210\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q2.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"479\" height=\"104\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q2.png 562w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q2-300x65.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q2-480x104.png 480w\" sizes=\"auto, (max-width: 479px) 100vw, 479px\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<\/strong><br \/>\n<strong>(i) (3 + \u221a3)(2 + \u221a2)<br \/>\n<\/strong>\u21d2 2(3 + \u221a3) + \u221a2(3 + \u221a3)<br \/>\n\u21d2 6 + 2\u221a3 + 3\u221a2 + \u221a6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) (3 + \u221a3)(3 &#8211; \u221a3 )<br \/>\n<\/strong>\u21d2 (3)<sup>2<\/sup> \u2013 (\u221a3)<sup>2<\/sup><br \/>\n\u21d2 9 &#8211; 3<br \/>\n\u21d2 6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) (\u221a5 + \u221a2)<sup>2<\/sup><br \/>\n<\/strong>\u21d2 (\u221a5)<sup>2<\/sup>\u00a0+ (\u221a2)<sup>2<\/sup>\u00a0+ 2(\u221a5)(\u221a2)<br \/>\n\u21d2 5 + 2 + 2\u221a10<br \/>\n\u21d2 7 + 2\u221a10<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) (\u221a5 &#8211; \u221a2)(\u221a5 + \u221a2)<br \/>\n<\/strong>\u21d2\u00a0 (\u221a5)<sup>2<\/sup>\u00a0\u2013 (\u221a2)<sup>2<\/sup><br \/>\n\u21d2\u00a0 5 \u2013 2<br \/>\n\u21d2\u00a0 3<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>3. Recall, \u03c0 is defined as the ratio of the circumference (say c) of a circle to its diameter, (say d). That is, \u03c0 = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{c}{d}}\" alt=\"\\mathbf{\\frac{c}{d}}\" align=\"absmiddle\" \/>. This seems to contradict the fact that \u03c0 is irrational. How will you resolve this contradiction?<br \/>\n<\/strong><strong>Answer &#8211; <\/strong>When we measure the length of a line with a scale or with any other device, we only get an approximate ational value, i.e. c and d both are irrational.<br \/>\n\u2234 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{c}{d}\" alt=\"\\frac{c}{d}\" align=\"absmiddle\" \/> is irrational and hence \u03c0 is irrational.<br \/>\nThus, there is no contradiction in saying that it is irrational.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. Represent (<img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\sqrt{9.3}}\" alt=\"\\mathbf{\\sqrt{9.3}}\" align=\"absmiddle\" \/>) on the number line.<br \/>\n<\/strong><strong>Answer &#8211;<\/strong>\u00a0 Let&#8217;s look into the steps below to represent <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9.3}\" alt=\"\\sqrt{9.3}\" align=\"absmiddle\" \/> on the number line.<br \/>\n<strong>Step 1 &#8211; <\/strong>Draw a line and take AB = 9.3 units on it.<br \/>\n<strong>Step 2 &#8211;<\/strong>\u00a0From B, measure a distance of 1 unit and mark C on the number line. Mark the midpoint of AC as O.<br \/>\n<strong>Step 3 &#8211;<\/strong>\u00a0With \u2018O\u2019 as center and OC as radius, draw a semicircle.<br \/>\n<strong>Step 4 &#8211; <\/strong>At B, draw a perpendicular to cut the semicircle at D.<br \/>\n<strong>Step 5 &#8211;<\/strong> With B as a center and BD as radius draw an arc to cut the number line at E. Thus, taking B as the origin the distance BE = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9.3}\" alt=\"\\sqrt{9.3}\" align=\"absmiddle\" \/><br \/>\nTherefore, point E represents <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9.3}\" alt=\"\\sqrt{9.3}\" align=\"absmiddle\" \/>\u00a0 on the number line.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4211\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q4.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"503\" height=\"307\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q4.png 591w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q4-300x183.png 300w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q4-480x293.png 480w\" sizes=\"auto, (max-width: 503px) 100vw, 503px\" \/><br \/>\nLet&#8217;s look at the proof shown below.<\/span><br \/>\n<span style=\"color: #000000;\">AB = 9.3, BC = 1<\/span><br \/>\n<span style=\"color: #000000;\">AC = AB + BC = 10.3<\/span><br \/>\n<span style=\"color: #000000;\">OC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{AC}{2}\" alt=\"\\frac{AC}{2}\" align=\"absmiddle\" \/> = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{10.3}{2}\" alt=\"\\frac{10.3}{2}\" align=\"absmiddle\" \/> = 5.15<\/span><br \/>\n<span style=\"color: #000000;\">OC = OD = 5.15<\/span><br \/>\n<span style=\"color: #000000;\">OB = OC \u2013 BC = 5.15 &#8211; 1 = 4.15<\/span><br \/>\n<span style=\"color: #000000;\">In right-angled \u2206OBD, using Pythagoras theorem we have, <\/span><br \/>\n<span style=\"color: #000000;\">BD<sup>2<\/sup> = OD<sup>2<\/sup> &#8211; OB<sup>2<\/sup> <\/span><br \/>\n<span style=\"color: #000000;\">\u27f9 (5.15)<sup>2<\/sup> &#8211; (4.15)<sup>2<\/sup> <\/span><br \/>\n<span style=\"color: #000000;\">\u27f9 (5.15 + 4.15)(5.15 &#8211; 4.15)\u00a0 \u00a0 \u00a0 \u00a0 \u00a0[Using a\u00b2 &#8211; b\u00b2 = (a + b)(a &#8211; b)] <\/span><br \/>\n<span style=\"color: #000000;\">\u27f9 9.3 \u00d7 1 <\/span><br \/>\n<span style=\"color: #000000;\">\u27f9 9.3 <\/span><br \/>\n<span style=\"color: #000000;\">Hence, BD = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9.3}\" alt=\"\\sqrt{9.3}\" align=\"absmiddle\" \/> = BE [Since they are the radii of the same circle] <\/span><br \/>\n<span style=\"color: #000000;\">Thus, we can say point E represents <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{9.3}\" alt=\"\\sqrt{9.3}\" align=\"absmiddle\" \/> on the number line.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. Rationalize\u00a0the denominators of the following:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-4208\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q5.png\" alt=\"NCERT Class 9 Solutions Maths\" width=\"373\" height=\"118\" srcset=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q5.png 436w, https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q5-300x95.png 300w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Answer &#8211;<\/strong><br \/>\n<strong>(i) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{\\sqrt{7}}}\" alt=\"\\mathbf{\\frac{1}{\\sqrt{7}}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>Multiply and divide <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{\\sqrt{7}}\" alt=\"\\frac{1}{\\sqrt{7}}\" align=\"absmiddle\" \/>\u00a0 by <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{7}\" alt=\"\\sqrt{7}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{\\sqrt{7}}\" alt=\"\\frac{1}{\\sqrt{7}}\" align=\"absmiddle\" \/>\u00a0 \u00d7 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{7}}{\\sqrt{7}}\" alt=\"\\frac{\\sqrt{7}}{\\sqrt{7}}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{7}}{7}\" alt=\"\\frac{\\sqrt{7}}{7}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{\\sqrt{7}-\\sqrt{6}}}\" alt=\"\\mathbf{\\frac{1}{\\sqrt{7}-\\sqrt{6}}}\" align=\"absmiddle\" \/><br \/>\n<\/strong>Dividing and multiplying by \u221a7 + \u221a6, we get<br \/>\n\u21d2\u00a0 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{\\sqrt{7}-\\sqrt{6}}&amp;space;\\times&amp;space;\\frac{\\sqrt{7}&amp;space;+&amp;space;\\sqrt{6}}{\\sqrt{7}&amp;space;+&amp;space;\\sqrt{6}}\" alt=\"\\frac{1}{\\sqrt{7}-\\sqrt{6}} \\times \\frac{\\sqrt{7} + \\sqrt{6}}{\\sqrt{7} + \\sqrt{6}}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{7}+\\sqrt{6}}{(\\sqrt{7})^{2}-(\\sqrt{6})^{2}}\" alt=\"\\frac{\\sqrt{7}+\\sqrt{6}}{(\\sqrt{7})^{2}-(\\sqrt{6})^{2}}\" width=\"113\" height=\"48\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 using the property, (a + b)(a &#8211; b) = a<sup>2 <\/sup>&#8211; b<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{7}+\\sqrt{6}}{7-6}\" alt=\"\\frac{\\sqrt{7}+\\sqrt{6}}{7-6}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{7}+\\sqrt{6}}{1}\" alt=\"\\frac{\\sqrt{7}+\\sqrt{6}}{1}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 \u221a7 + \u221a6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{\\sqrt{5}&amp;space;+&amp;space;\\sqrt{2}}}\" alt=\"\\mathbf{\\frac{1}{\\sqrt{5} + \\sqrt{2}}}\" align=\"absmiddle\" \/><br \/>\n<\/strong><\/span><span style=\"color: #000000;\">Dividing and multiplying by \u221a5 &#8211; \u221a2, we get<br \/>\n\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{\\sqrt{5}+\\sqrt{2}}&amp;space;\\times&amp;space;\\frac{\\sqrt{5}&amp;space;-&amp;space;\\sqrt{2}}{\\sqrt{5}&amp;space;-&amp;space;\\sqrt{2}}\" alt=\"\\frac{1}{\\sqrt{5}+\\sqrt{2}} \\times \\frac{\\sqrt{5} - \\sqrt{2}}{\\sqrt{5} - \\sqrt{2}}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{5}-\\sqrt{2}}{(\\sqrt{5})^{2}-(\\sqrt{2})^{2}}\" alt=\"\\frac{\\sqrt{5}-\\sqrt{2}}{(\\sqrt{5})^{2}-(\\sqrt{2})^{2}}\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 using the property, (a + b)(a &#8211; b) = a<sup>2 <\/sup>&#8211; b<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{5}&amp;space;-&amp;space;\\sqrt{2}}{5-2}\" alt=\"\\frac{\\sqrt{5} - \\sqrt{2}}{5-2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{5}&amp;space;-&amp;space;\\sqrt{2}}{3}\" alt=\"\\frac{\\sqrt{5} - \\sqrt{2}}{3}\" align=\"absmiddle\" \/><br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\mathbf{\\frac{1}{\\sqrt{7}-2}}\" alt=\"\\mathbf{\\frac{1}{\\sqrt{7}-2}}\" width=\"59\" height=\"42\" align=\"absmiddle\" \/><br \/>\n<\/strong>Multiply and divide by (\u221a7 + 2), we get<br \/>\n<\/span><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{1}{\\sqrt{7}&amp;space;-&amp;space;2}&amp;space;\\times&amp;space;\\frac{\\sqrt{7}&amp;space;+&amp;space;2}{\\sqrt{7}&amp;space;+&amp;space;2}\" alt=\"\\frac{1}{\\sqrt{7} - 2} \\times \\frac{\\sqrt{7} + 2}{\\sqrt{7} + 2}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{7}&amp;space;+&amp;space;2}{(\\sqrt{7})^{2}-(2)^{2}}\" alt=\"\\frac{\\sqrt{7} + 2}{(\\sqrt{7})^{2}-(2)^{2}}\" width=\"98\" height=\"48\" align=\"absmiddle\" \/>\u00a0 \u00a0 \u00a0 \u00a0 using the property, (a + b)(a &#8211; b) = a<sup>2 <\/sup>&#8211; b<sup>2<\/sup><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{7}&amp;space;+&amp;space;2}{7-&amp;space;4}\" alt=\"\\frac{\\sqrt{7} + 2}{7- 4}\" width=\"56\" height=\"41\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\">\u21d2 <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{\\sqrt{7}&amp;space;+&amp;space;2}{3}\" alt=\"\\frac{\\sqrt{7} + 2}{3}\" align=\"absmiddle\" \/><\/span><\/p>\n<p style=\"text-align: justify;\">\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 9 Maths\u00a0 Chapter &#8211; 1 (Number Systems )\u00a0 The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter &#8211; 1 Number Systems\u00a0Exercise 1.5 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 1: Number Systems NCERT Solution Class 9 Maths Ex &#8211; 1.1 NCERT Solution [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[698],"tags":[699,702,186,700,701,5],"class_list":["post-4025","post","type-post","status-publish","format-standard","hentry","category-class-9-maths","tag-class-9th-chapter-1-number-systems-in-english","tag-ncert-solution-class-9","tag-ncert-solutions","tag-ncert-solutions-class-9-maths-chapter-1-in-english","tag-ncert-solutions-class-9-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5 | TheExamPillar NCERT<\/title>\n<meta name=\"description\" content=\"NCERT Solutions Class 9 Maths\u00a0Chapter - 1 (Number Systems )\u00a0The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter - 1 Number Systems\u00a0Exercise 1.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 1.5\u00a0\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5\" \/>\n<meta property=\"og:description\" content=\"NCERT Solutions Class 9 Maths\u00a0Chapter - 1 (Number Systems )\u00a0The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter - 1 Number Systems\u00a0Exercise 1.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 1.5\u00a0\" \/>\n<meta property=\"og:url\" content=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/\" \/>\n<meta property=\"og:site_name\" content=\"TheExamPillar NCERT\" \/>\n<meta property=\"article:published_time\" content=\"2023-02-01T06:54:29+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png\" \/>\n<meta name=\"author\" content=\"Admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@exampillar\" \/>\n<meta name=\"twitter:site\" content=\"@exampillar\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"11 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/\"},\"author\":{\"name\":\"Admin\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#\\\/schema\\\/person\\\/521fbdbd2eb8621382a3096b5e3ecaf1\"},\"headline\":\"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5\",\"datePublished\":\"2023-02-01T06:54:29+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/\"},\"wordCount\":507,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#\\\/schema\\\/person\\\/521fbdbd2eb8621382a3096b5e3ecaf1\"},\"image\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2023\\\/01\\\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png\",\"keywords\":[\"Class 9th Chapter 1 Number Systems in English\",\"Ncert Solution Class 9\",\"NCERT Solutions\",\"NCERT Solutions Class 9 Maths Chapter 1 in english\",\"NCERT Solutions Class 9 Maths in English\",\"NCERT Solutions in English\"],\"articleSection\":[\"Class 9 Maths\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/\",\"url\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/\",\"name\":\"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5 | TheExamPillar NCERT\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2023\\\/01\\\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png\",\"datePublished\":\"2023-02-01T06:54:29+00:00\",\"description\":\"NCERT Solutions Class 9 Maths\u00a0Chapter - 1 (Number Systems )\u00a0The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter - 1 Number Systems\u00a0Exercise 1.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 1.5\u00a0\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/#primaryimage\",\"url\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2023\\\/01\\\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png\",\"contentUrl\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2023\\\/01\\\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png\",\"width\":651,\"height\":132,\"caption\":\"NCERT Class 9 Solutions Maths\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#website\",\"url\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/\",\"name\":\"TheExamPillar NCERT\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#\\\/schema\\\/person\\\/521fbdbd2eb8621382a3096b5e3ecaf1\"},\"alternateName\":\"NCERT Solution\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":[\"Person\",\"Organization\"],\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/#\\\/schema\\\/person\\\/521fbdbd2eb8621382a3096b5e3ecaf1\",\"name\":\"Admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2022\\\/07\\\/cropped-ExamPillar-PNG.png\",\"url\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2022\\\/07\\\/cropped-ExamPillar-PNG.png\",\"contentUrl\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2022\\\/07\\\/cropped-ExamPillar-PNG.png\",\"width\":512,\"height\":512,\"caption\":\"Admin\"},\"logo\":{\"@id\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/wp-content\\\/uploads\\\/2022\\\/07\\\/cropped-ExamPillar-PNG.png\"},\"sameAs\":[\"https:\\\/\\\/theexampillar.com\\\/ncert\"],\"url\":\"https:\\\/\\\/theexampillar.com\\\/ncert\\\/author\\\/ncert_eng_vikram\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5 | TheExamPillar NCERT","description":"NCERT Solutions Class 9 Maths\u00a0Chapter - 1 (Number Systems )\u00a0The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter - 1 Number Systems\u00a0Exercise 1.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 1.5\u00a0","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/","og_locale":"en_US","og_type":"article","og_title":"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5","og_description":"NCERT Solutions Class 9 Maths\u00a0Chapter - 1 (Number Systems )\u00a0The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter - 1 Number Systems\u00a0Exercise 1.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 1.5\u00a0","og_url":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/","og_site_name":"TheExamPillar NCERT","article_published_time":"2023-02-01T06:54:29+00:00","og_image":[{"url":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png","type":"","width":"","height":""}],"author":"Admin","twitter_card":"summary_large_image","twitter_creator":"@exampillar","twitter_site":"@exampillar","twitter_misc":{"Written by":"Admin","Est. reading time":"11 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/#article","isPartOf":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/"},"author":{"name":"Admin","@id":"https:\/\/theexampillar.com\/ncert\/#\/schema\/person\/521fbdbd2eb8621382a3096b5e3ecaf1"},"headline":"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5","datePublished":"2023-02-01T06:54:29+00:00","mainEntityOfPage":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/"},"wordCount":507,"commentCount":0,"publisher":{"@id":"https:\/\/theexampillar.com\/ncert\/#\/schema\/person\/521fbdbd2eb8621382a3096b5e3ecaf1"},"image":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/#primaryimage"},"thumbnailUrl":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png","keywords":["Class 9th Chapter 1 Number Systems in English","Ncert Solution Class 9","NCERT Solutions","NCERT Solutions Class 9 Maths Chapter 1 in english","NCERT Solutions Class 9 Maths in English","NCERT Solutions in English"],"articleSection":["Class 9 Maths"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/","url":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/","name":"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5 | TheExamPillar NCERT","isPartOf":{"@id":"https:\/\/theexampillar.com\/ncert\/#website"},"primaryImageOfPage":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/#primaryimage"},"image":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/#primaryimage"},"thumbnailUrl":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png","datePublished":"2023-02-01T06:54:29+00:00","description":"NCERT Solutions Class 9 Maths\u00a0Chapter - 1 (Number Systems )\u00a0The NCERT Solutions in English Language for Class 9 Mathematics\u00a0Chapter - 1 Number Systems\u00a0Exercise 1.5 has been provided here to help the students in solving the questions from this exercise.\u00a0Exercise - 1.5\u00a0","breadcrumb":{"@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/#primaryimage","url":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png","contentUrl":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2023\/01\/NCERT-Solutions-Class-9-Maths-Ex-1.5-Q1.png","width":651,"height":132,"caption":"NCERT Class 9 Solutions Maths"},{"@type":"BreadcrumbList","@id":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-9-maths-chapter-1-number-systems-ex-1-5\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/theexampillar.com\/ncert\/"},{"@type":"ListItem","position":2,"name":"NCERT Solutions Class 9 Maths Chapter 1 Number Systems Ex 1.5"}]},{"@type":"WebSite","@id":"https:\/\/theexampillar.com\/ncert\/#website","url":"https:\/\/theexampillar.com\/ncert\/","name":"TheExamPillar NCERT","description":"","publisher":{"@id":"https:\/\/theexampillar.com\/ncert\/#\/schema\/person\/521fbdbd2eb8621382a3096b5e3ecaf1"},"alternateName":"NCERT Solution","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/theexampillar.com\/ncert\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":["Person","Organization"],"@id":"https:\/\/theexampillar.com\/ncert\/#\/schema\/person\/521fbdbd2eb8621382a3096b5e3ecaf1","name":"Admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/cropped-ExamPillar-PNG.png","url":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/cropped-ExamPillar-PNG.png","contentUrl":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/cropped-ExamPillar-PNG.png","width":512,"height":512,"caption":"Admin"},"logo":{"@id":"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/07\/cropped-ExamPillar-PNG.png"},"sameAs":["https:\/\/theexampillar.com\/ncert"],"url":"https:\/\/theexampillar.com\/ncert\/author\/ncert_eng_vikram\/"}]}},"_links":{"self":[{"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/posts\/4025","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/comments?post=4025"}],"version-history":[{"count":6,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/posts\/4025\/revisions"}],"predecessor-version":[{"id":4938,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/posts\/4025\/revisions\/4938"}],"wp:attachment":[{"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/media?parent=4025"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/categories?post=4025"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/theexampillar.com\/ncert\/wp-json\/wp\/v2\/tags?post=4025"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}