{"id":3131,"date":"2022-12-06T07:36:52","date_gmt":"2022-12-06T07:36:52","guid":{"rendered":"https:\/\/theexampillar.com\/ncert\/?p=3131"},"modified":"2023-01-31T06:53:41","modified_gmt":"2023-01-31T06:53:41","slug":"ncert-solutions-class-8-maths-chapter-6-squares-and-square-roots-ex-6-4","status":"publish","type":"post","link":"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-6-squares-and-square-roots-ex-6-4\/","title":{"rendered":"NCERT Solutions Class 8 Maths Chapter 6 Squares and Square Roots Ex 6.4"},"content":{"rendered":"<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">NCERT Solutions Class 8 Mathematics\u00a0<\/span><br \/>\n<span style=\"color: #000000; font-family: georgia, palatino, serif;\">Chapter &#8211; 6 (Squares and Square)\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 8 Mathematics <strong>Chapter &#8211; 6 Squares and Square <\/strong>Exercise 6.4 has been provided here to help the students in solving the questions from this exercise.\u00a0<\/span><\/p>\n<h4><span style=\"color: #000000;\"><strong>Chapter 6: Squares and Square Roots<\/strong><\/span><\/h4>\n<ul>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-6-squares-and-square-roots-ex-6-1\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 6.1<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-6-squares-and-square-roots-ex-6-2\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 6.2<\/a><\/li>\n<li><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths-chapter-6-squares-and-square-roots-ex-6-3\" target=\"_blank\" rel=\"noopener\">NCERT Solution Class 8 Maths Ex &#8211; 6.3<\/a><\/li>\n<\/ul>\n<h2 style=\"text-align: center;\"><span style=\"color: #000000; font-family: georgia, palatino, serif;\">Exercise &#8211; 6.4\u00a0<\/span><\/h2>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>1. Find the square root of each of the following numbers by Division method.<\/strong><br \/>\n<strong>(i)<\/strong> 2304\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>(ii)<\/strong> 4489\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>(iii)<\/strong> 3481<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(iv)<\/strong> 529\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>(v)<\/strong> 3249\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<strong>(vi)<\/strong> 1369<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(vii)<\/strong> 5776\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<strong>(viii)<\/strong> 7921\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<strong>(ix)<\/strong> 576<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(x)<\/strong> 1024\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<strong>(xi)<\/strong> 3136\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 <strong>(xii)<\/strong> 900<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) 2304<\/strong><br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3167\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1i.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"116\" height=\"200\" \/><br \/>\n\u2234 \u221a2304 = 48<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 4489<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3168\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1ii.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"124\" height=\"200\" \/><br \/>\n<\/strong>\u2234 \u221a4489 = 67<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) 3481<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3169\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1iii.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"108\" height=\"200\" \/><br \/>\n<\/strong>\u2234 \u221a3481 = 59<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) 529<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3170\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1iv.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"97\" height=\"200\" \/><br \/>\n<\/strong>\u2234 \u221a529 = 23<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) 3249<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3172\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1v.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"99\" height=\"200\" \/><br \/>\n<\/strong>\u2234 \u221a3249 = 57<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vi) 1369<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3173\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1vi.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"87\" height=\"200\" \/><br \/>\n<\/strong>\u2234 \u221a1369 = 37<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(vii) 5776<br \/>\n<\/strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3174\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1vii.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"98\" height=\"200\" \/><br \/>\n\u2234 \u221a5776 = 76<strong><br \/>\n<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(viii) 7921<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3175\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1viii.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"109\" height=\"200\" \/><br \/>\n<\/strong>\u2234 \u221a7921 = 89<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ix) 576<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3171\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1ix.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"89\" height=\"200\" \/><br \/>\n<\/strong>\u2234 \u221a576 = 24<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(x) 1024<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3176\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1x.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"82\" height=\"200\" \/><br \/>\n<\/strong>\u2234 \u221a1024 = 32<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(xi) 3136<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3177\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1xi.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"95\" height=\"200\" \/><br \/>\n<\/strong>\u2234 \u221a3136 = 56<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(xii) 900<br \/>\n<\/strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3178\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-1xii.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"75\" height=\"108\" \/><br \/>\n\u2234 \u221a900 = 30<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>2. Find the number of digits in the square root of each of the following numbers (without any <\/strong><strong>calculation).<br \/>\n<\/strong><strong>(i)<\/strong> 64 <\/span><br \/>\n<span style=\"color: #000000;\"><strong>(ii)<\/strong> 144<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(iii)<\/strong> 4489 <\/span><br \/>\n<span style=\"color: #000000;\"><strong>(iv)<\/strong> 27225<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(v)<\/strong> 390625<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) 64<br \/>\n<\/strong>Number (n) of digits in 64 = 2 which is even.<\/span><br \/>\n<span style=\"color: #000000;\">\u2234 Number of digits in the square root of 64.<\/span><br \/>\n<span id=\"MathJax-Element-1-Frame\" class=\"MathJax\" style=\"color: #000000;\" tabindex=\"0\"><span id=\"MathJax-Span-1\" class=\"math\"><span id=\"MathJax-Span-2\" class=\"mrow\"><span id=\"MathJax-Span-3\" class=\"mfrac\"><span id=\"MathJax-Span-5\" class=\"mn\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{n}{2}&amp;space;=&amp;space;\\frac{2}{2}\" alt=\"\\frac{n}{2} = \\frac{2}{2}\" align=\"absmiddle\" \/> <\/span><\/span><span id=\"MathJax-Span-10\" class=\"mo\">= <\/span><span id=\"MathJax-Span-11\" class=\"mn\">1<\/span><\/span><\/span><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii) 144<\/strong><\/span><br \/>\n<span style=\"color: #000000;\">Number (n) of digits in 144 = 3 which is<\/span><br \/>\n<span style=\"color: #000000;\">\u2234 Number of digits in the square root of 144.\u00a0<\/span><br \/>\n<span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{n+1}{2}&amp;space;=&amp;space;\\frac{3+1}{2}&amp;space;=&amp;space;\\frac{4}{2}\" alt=\"\\frac{n+1}{2} = \\frac{3+1}{2} = \\frac{4}{2}\" align=\"absmiddle\" \/> = <span id=\"MathJax-Element-2-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-12\" class=\"math\"><span id=\"MathJax-Span-13\" class=\"mrow\"><span id=\"MathJax-Span-32\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii) 4489<br \/>\n<\/strong>Number (n) of digits in 4489 = 4 which is even. <\/span><br \/>\n<span style=\"color: #000000;\">\u2234 Number of digits in the square root of 4489.<\/span><br \/>\n<span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{n}{2}&amp;space;=&amp;space;\\frac{4}{2}&amp;space;=\" alt=\"\\frac{n}{2} = \\frac{4}{2} =\" align=\"absmiddle\" \/> \u00a0<span id=\"MathJax-Element-3-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-33\" class=\"math\"><span id=\"MathJax-Span-34\" class=\"mrow\"><span id=\"MathJax-Span-43\" class=\"mn\">2<\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iv) 27225<\/strong><\/span><br \/>\n<span style=\"color: #000000;\">Number (n) of digits in 27225 = 5 which is odd. <\/span><br \/>\n<span style=\"color: #000000;\">\u2234 Number of digits in the square root of 27225. <\/span><br \/>\n<span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{n+1}{2}&amp;space;=&amp;space;\\frac{5+1}{2}&amp;space;=\\frac{6}{2}\" alt=\"\\frac{n+1}{2} = \\frac{5+1}{2} =\\frac{6}{2}\" align=\"absmiddle\" \/> = 3 <\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(v) 390625<\/strong><\/span><br \/>\n<span style=\"color: #000000;\">Number (n) of digits in 390625 = 6 which is even.<\/span><br \/>\n<span style=\"color: #000000;\">\u2234 Number of digits in the square root of 390625.<\/span><br \/>\n<span style=\"color: #000000;\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\frac{n}{2}&amp;space;=&amp;space;\\frac{6}{2}&amp;space;=\" alt=\"\\frac{n}{2} = \\frac{6}{2} =\" align=\"absmiddle\" \/> \u00a0<span id=\"MathJax-Element-5-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-65\" class=\"math\"><span id=\"MathJax-Span-66\" class=\"mrow\"><span id=\"MathJax-Span-75\" class=\"mn\">3<\/span><\/span><\/span><\/span><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>3. Find the square root of the following decimal numbers.<br \/>\n<\/strong><strong>(i)<\/strong>\u00a02.56<br \/>\n<strong>(ii)<\/strong>\u00a07.29<br \/>\n<strong>(iii)<\/strong>\u00a051.84<br \/>\n<strong>(iv)<\/strong>\u00a042.25<br \/>\n<strong>(v)<\/strong>\u00a031.36<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(i)\u00a02.56<\/strong><\/span><br \/>\n<span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3179\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-3i.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"90\" height=\"200\" \/><\/span><br \/>\n<span style=\"color: #000000;\">\u2234 \u221a2.56 = 1.6<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(ii)\u00a07.29<\/strong><\/span><br \/>\n<span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3180\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-3ii.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"95\" height=\"200\" \/><\/span><br \/>\n<span style=\"color: #000000;\">\u2234 \u221a7.29 = 2.7<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iii)\u00a051.84<\/strong><\/span><br \/>\n<span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3181\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-3iii.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"110\" height=\"200\" \/><\/span><br \/>\n<span style=\"color: #000000;\">\u2234 \u221a51.84 = 7.2<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(iv)\u00a042.25<\/strong><\/span><br \/>\n<span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3182\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-3iv.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"93\" height=\"200\" \/><\/span><br \/>\n<span style=\"color: #000000;\">\u2234 \u221a42.25 = 6.5<\/span><\/p>\n<p><span style=\"color: #000000;\"><strong>(v)\u00a031.36<\/strong><\/span><br \/>\n<span style=\"color: #000000;\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3183\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-3v.jpeg\" alt=\"NCERT Maths Solutions Class 8\" width=\"97\" height=\"200\" \/><\/span><br \/>\n<span style=\"color: #000000;\">\u2234 \u221a31.36 = 5.6<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>4. Find the least number which must be subtracted from each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.<br \/>\n<\/strong><strong>(i)\u00a0<\/strong>402<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(ii)<\/strong>\u00a01989<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(iii)<\/strong>\u00a03250<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(iv)<\/strong>\u00a0825<\/span><br \/>\n<span style=\"color: #000000;\"><strong>(v)<\/strong>\u00a04000<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i)\u00a0402<br \/>\n<\/strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3184\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-4i.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"90\" height=\"115\" \/><br \/>\n\u2234 We must subtracted 2 from 402 to get a perfect square.<br \/>\nNew number = 402 \u2013 2 = 400<br \/>\n\u2234 \u221a400 = 20<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 1989<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3185\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-4ii.jpg\" alt=\"NCERT Maths Solutions Class 8\" width=\"87\" height=\"200\" \/><br \/>\n<\/strong>\u2234 We must subtracted 53 from 1989 to get a perfect square.<br \/>\nNew number = 1989 \u2013 53 = 1936<br \/>\n\u2234 \u221a1936 = 44<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii)\u00a03250<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3186\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-4iii.jpg\" alt=\"NCERT Maths Solutions Class 8\" width=\"93\" height=\"200\" \/><br \/>\n<\/strong>\u2234 We must subtracted 1 from 3250 to get a perfect square.<br \/>\nNew number = 3250 \u2013 1 = 3249<br \/>\n\u2234 \u221a3249 = 57<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) 825<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3187\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-4iv.jpg\" alt=\"NCERT Maths Solutions Class 8\" width=\"86\" height=\"200\" \/><br \/>\n<\/strong>\u2234 We must subtracted 41 from 825 to get a perfect square.<br \/>\nNew number = 825 \u2013 41 = 784<br \/>\n\u2234 \u221a784 = 28<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v)\u00a04000<br \/>\n<\/strong><img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3188\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-4v.jpg\" alt=\"NCERT Maths Solutions Class 8\" width=\"93\" height=\"200\" \/><br \/>\n\u2234 We must subtracted 31 from 4000 to get a perfect square. New number = 4000 \u2013 31 = 3969<br \/>\n\u2234 \u221a3969 = 63<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>5. Find the least number which must be added to each of the following numbers so as to get a perfect square. Also find the square root of the perfect square so obtained.<br \/>\n<\/strong><strong>(i) <\/strong>525<strong><br \/>\n<\/strong><strong>(ii) <\/strong>1750<strong><br \/>\n<\/strong><strong>(iii)<\/strong> 252<strong><br \/>\n<\/strong><strong>(iv) <\/strong>1825<strong><br \/>\n<\/strong><strong>(v) <\/strong>6412<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(i) 525<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3189\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-5i.jpg\" alt=\"NCERT Maths Solutions Class 8\" width=\"93\" height=\"200\" \/><br \/>\n<\/strong>This shows that (22)<sup>2<\/sup> &lt; 525<br \/>\nNext perfect square is 23<sup>2<\/sup> = 529<br \/>\nHence, the number to be added is 23<sup>2<\/sup> &#8211; 525 = 529 &#8211; 525 = 4<br \/>\nTherefore, the perfect square so obtained is 525 + 4 =\u00a0529<br \/>\nHence , \u221a529 = 23.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(ii) 1750<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3190\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-5ii.jpg\" alt=\"NCERT Maths Solutions Class 8\" width=\"92\" height=\"200\" \/><br \/>\n<\/strong><\/span><\/p>\n<p><span style=\"color: #000000;\">This shows that (41)<sup>2<\/sup> &lt; 1750<br \/>\nNext perfect square is 42<sup>2<\/sup> = 1764<br \/>\nHence, the number to be added is 42<sup>2<\/sup> &#8211; 1750 = 1764 &#8211; 1750 = 14<br \/>\nTherefore, the perfect square so obtained is 1750 + 14 = 1764<br \/>\nHence , \u221a1764 = 42.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iii) 252<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3191\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-5iii.jpg\" alt=\"NCERT Maths Solutions Class 8\" width=\"88\" height=\"200\" \/><br \/>\n<\/strong>This shows that (15)<sup>2<\/sup> &lt; 252<br \/>\nNext perfect square is 16<sup>2<\/sup> = 256<br \/>\nHence, the number to be added is 16<sup>2<\/sup> &#8211; 252 = 256 &#8211; 252 = 4<br \/>\nTherefore, the perfect square so obtained is 252 + 4 = 256<br \/>\nHence , \u221a256 = 16.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(iv) 1825<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3192\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-5iv.jpg\" alt=\"NCERT Maths Solutions Class 8\" width=\"81\" height=\"200\" \/><br \/>\n<\/strong>This shows that (42)<sup>2<\/sup> &lt; 1825<br \/>\nNext perfect square is 43<sup>2<\/sup> = 1849<br \/>\nHence, the number to be added is 43<sup>2<\/sup> &#8211; 1825 = 1849 &#8211; 1825 = 24<br \/>\nTherefore, the perfect square so obtained is 1825 + 24 = 1849<br \/>\nHence , \u221a1849 = 43.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>(v) 6412<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-3193\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-5v.jpg\" alt=\"NCERT Maths Solutions Class 8\" width=\"91\" height=\"157\" \/><br \/>\n<\/strong>This shows that (80)<sup>2<\/sup> &lt; 6412<br \/>\nNext perfect square is 81<sup>2<\/sup> = 6561<br \/>\nHence, the number to be added is 81<sup>2<\/sup> &#8211; 6412 = 6561 &#8211; 6412 = 149<br \/>\nTherefore, the perfect square so obtained is 6412 + 149 = 6561<br \/>\nHence , \u221a6561 = 81.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>6. Find the length of the side of a square whose area is 441 m<sup>2<\/sup>.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong>Area of the square = 441\u00a0<span id=\"MathJax-Element-7-Frame\" class=\"MathJax\" tabindex=\"0\"><span id=\"MathJax-Span-85\" class=\"math\"><span id=\"MathJax-Span-86\" class=\"mrow\"><span id=\"MathJax-Span-87\" class=\"msubsup\"><span id=\"MathJax-Span-88\" class=\"texatom\"><span id=\"MathJax-Span-89\" class=\"mrow\"><span id=\"MathJax-Span-90\" class=\"mi\">m<\/span><\/span><\/span><sup><span id=\"MathJax-Span-91\" class=\"texatom\"><span id=\"MathJax-Span-92\" class=\"mrow\"><span id=\"MathJax-Span-93\" class=\"mn\">2<\/span><\/span><\/span><\/sup><\/span><\/span><\/span><\/span><br \/>\n\u2234 Length of the side of the square = \u221a441 m<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3194\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-6i.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"100\" height=\"213\" \/><br \/>\n\u21d2 \u221a441 m = 21.<br \/>\n\u2234 The length of each side is = 21 m.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>7. In a right triangle ABC, \u2220B = 90\u00b0.<br \/>\n<\/strong><strong>a.<\/strong> If AB = 6 cm, BC = 8 cm, find AC<br \/>\n<strong>b.<\/strong> If AC = 13 cm, BC = 5 cm, find AB<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211;<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>a. If AB = 6 cm, BC = 8 cm, find AC<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3195\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-7i.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"209\" height=\"289\" \/><br \/>\n<\/strong>Given, AB = 6 cm, BC = 8 cm<br \/>\nLet AC be x cm.<br \/>\n\u2234 AC<sup>2<\/sup> = AB<sup>2<\/sup> + BC<sup>2<\/sup><br \/>\nAC = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{AB^2&amp;space;+&amp;space;BC^2}\" alt=\"\\sqrt{AB^2 + BC^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{6^2&amp;space;+&amp;space;8^2}\" alt=\"\\sqrt{6^2 + 8^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{36+64}\" alt=\"\\sqrt{36+64}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{100}\" alt=\"\\sqrt{100}\" align=\"absmiddle\" \/><br \/>\n= 10<br \/>\nHence, AC = 10 cm.<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>b. If AC = 13 cm, BC = 5 cm, find AB<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3196\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-7ii.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"205\" height=\"287\" \/><br \/>\n<\/strong>Given, AC = 13 cm, BC = 5 cm<br \/>\nLet AB be x cm.<br \/>\n\u2234 AC<sup>2<\/sup> = AB<sup>2<\/sup> + BC<sup>2<br \/>\n<\/sup>\u21d2 AC<sup>2<\/sup> \u2013 BC<sup>2<\/sup> = AB<sup>2<\/sup><br \/>\nAB = <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{AC^2&amp;space;-&amp;space;BC^2}\" alt=\"\\sqrt{AC^2 - BC^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{13^2&amp;space;-&amp;space;5^2}\" alt=\"\\sqrt{13^2 - 5^2}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{169-25}\" alt=\"\\sqrt{169-25}\" align=\"absmiddle\" \/><br \/>\n= <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\sqrt{144}\" alt=\"\\sqrt{144}\" align=\"absmiddle\" \/><br \/>\n= 12<br \/>\nHence, AB = 12 cm<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>8. A gardener has 1000 plants. He wants to plant these in such a way that the number of rows <\/strong><strong>and the number of columns remain same. Find the minimum number of plants he needs more for this.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong>Let the number of rows and column be, x.<br \/>\n\u2234 Total number of row and column= x \u00d7 x = x<sup>2<\/sup><br \/>\nx<sup>2<\/sup> = 1000<br \/>\n\u21d2 x = \u221a1000<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3197\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-8.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"115\" height=\"167\" \/><br \/>\nThis show that (31)<sup>2<\/sup> &lt; 1000<br \/>\nNext perfect square is 32<sup>2<\/sup> = 1024<br \/>\nHence, the minimum number of plants be need more for this = 1024 &#8211; 1000 = 24<br \/>\n<\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>9. There are 500 children in a school. For a P.T. drill they have to stand in such a manner that the number of rows is equal to number of columns. How many children would be left out in this arrangement.<\/strong><\/span><\/p>\n<p style=\"text-align: justify;\"><span style=\"color: #000000;\"><strong>Solution &#8211; <\/strong>Let the number of rows and column be, x.<br \/>\n\u2234 Total number of row and column= x \u00d7 x = x<sup>2<\/sup><br \/>\nx<sup>2<\/sup> = 500<br \/>\nx = \u221a500<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone size-full wp-image-3198\" src=\"https:\/\/theexampillar.com\/ncert\/wp-content\/uploads\/2022\/12\/NCERT-Solutions-Class-8-Maths-Ex-6.4-Q-9.png\" alt=\"NCERT Maths Solutions Class 8\" width=\"101\" height=\"172\" \/><br \/>\nHence, 16 children would be left out in the arrangement<\/span><\/p>\n<p>&nbsp;<\/p>\n<table style=\"width: 100%; border-collapse: collapse;\" border=\"1\">\n<tbody>\n<tr style=\"height: 32px;\">\n<td style=\"width: 100%; background-color: #f2e079; text-align: center; height: 32px;\"><span style=\"color: #ff0000; font-size: 14pt;\"><strong>NCERT Class 8<sup>th\u00a0<\/sup>Solution\u00a0<\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-english\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 English\u201d (Edit)\">NCERT Solutions Class 8 English<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-hindi\/\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Hindi<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-maths\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Maths\u201d (Edit)\">NCERT Solutions Class 8 Mathematics<\/a>\u00a0<\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><a href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-sanskrit-ruchira\/\" target=\"_blank\" rel=\"noopener\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\">NCERT Solutions Class 8 Sanskrit<\/span><\/strong><\/span><\/a><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<tr style=\"height: 28px;\">\n<td style=\"width: 100%; text-align: left; height: 28px;\"><span style=\"font-size: 14pt;\"><strong><span style=\"font-family: georgia, palatino, serif; font-size: 12pt;\"><a class=\"row-title\" href=\"https:\/\/theexampillar.com\/ncert\/ncert-solutions-class-8-social-science\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cNCERT Solutions Class 6 Social Science\u201d (Edit)\">NCERT Solutions Class 8 Social Science<\/a><\/span><\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>NCERT Solutions Class 8 Mathematics\u00a0 Chapter &#8211; 6 (Squares and Square)\u00a0 The NCERT Solutions in English Language for Class 8 Mathematics Chapter &#8211; 6 Squares and Square Exercise 6.4 has been provided here to help the students in solving the questions from this exercise.\u00a0 Chapter 6: Squares and Square Roots NCERT Solution Class 8 Maths [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[442],"tags":[454,455,445,5],"class_list":["post-3131","post","type-post","status-publish","format-standard","hentry","category-class-8-maths","tag-ncert-class-8-maths-chapter-6-squares-and-square-roots-in-english","tag-ncert-solutions-class-8-maths-chapter-6-in-english","tag-ncert-solutions-class-8-maths-in-english","tag-ncert-solutions-in-english"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v22.9 (Yoast SEO v27.5) - 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