{"id":29443,"date":"2022-01-31T19:40:29","date_gmt":"2022-01-31T14:10:29","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=29443"},"modified":"2022-04-25T15:17:06","modified_gmt":"2022-04-25T09:47:06","slug":"squares-and-square-roots-class-8-extra-questions-maths-chapter-6","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-8\/maths\/squares-and-square-roots-class-8-extra-questions-maths-chapter-6\/","title":{"rendered":"Squares and Square Roots Class 8 Extra Questions Maths Chapter 6"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\">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\" style=\"display: none;\"><label for=\"item\" 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ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-8\/maths\/squares-and-square-roots-class-8-extra-questions-maths-chapter-6\/#Squares_and_Square_Roots_Class_8_Extra_Questions_Maths_Chapter_6\" title=\"Squares and Square Roots Class 8 Extra Questions Maths Chapter 6\">Squares and Square Roots Class 8 Extra Questions Maths Chapter 6<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-8\/maths\/squares-and-square-roots-class-8-extra-questions-maths-chapter-6\/#Squares_and_Square_Roots_Class_8_Extra_Questions_Very_Short_Answer_Type\" title=\"Squares and Square Roots Class 8 Extra Questions Very Short Answer Type\">Squares and Square Roots Class 8 Extra Questions Very Short Answer Type<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-8\/maths\/squares-and-square-roots-class-8-extra-questions-maths-chapter-6\/#Squares_and_Square_Roots_Class_8_Extra_Questions_Short_Answer_Type\" title=\"Squares and Square Roots Class 8 Extra Questions Short Answer Type\">Squares and Square Roots Class 8 Extra Questions Short Answer Type<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/study-material\/cbse-notes\/class-8\/maths\/squares-and-square-roots-class-8-extra-questions-maths-chapter-6\/#Squares_and_Square_Roots_Class_8_Extra_Questions_Higher_Order_Thinking_Skills_HOTS\" title=\"Squares and Square Roots Class 8 Extra Questions Higher Order Thinking Skills (HOTS)\">Squares and Square Roots Class 8 Extra Questions Higher Order Thinking Skills (HOTS)<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Squares_and_Square_Roots_Class_8_Extra_Questions_Maths_Chapter_6\"><\/span>Squares and Square Roots Class 8 Extra Questions Maths Chapter 6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><strong>Extra Questions for Class 8 Maths Chapter 6 Squares and Square Roots<\/strong><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Squares_and_Square_Roots_Class_8_Extra_Questions_Very_Short_Answer_Type\"><\/span>Squares and Square Roots Class 8 Extra Questions Very Short Answer Type<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Question 1.<br \/>\nFind the perfect square numbers between 40 and 50.<br \/>\nSolution:<br \/>\nPerfect square numbers between 40 and 50 = 49.<\/p>\n<p>Question 2.<br \/>\nWhich of the following 24<sup>2<\/sup>, 49<sup>2<\/sup>, 77<sup>2<\/sup>, 131<sup>2<\/sup> or 189<sup>2<\/sup> end with digit 1?<br \/>\nSolution:<br \/>\nOnly 49<sup>2<\/sup>, 131<sup>2<\/sup> and 189<sup>2<\/sup> end with digit 1.<\/p>\n<p>Question 3.<br \/>\nFind the value of each of the following without calculating squares.<br \/>\n(i) 27<sup>2<\/sup> \u2013 26<sup>2<\/sup><br \/>\n(ii) 118<sup>2<\/sup> \u2013 117<sup>2<\/sup><br \/>\nSolution:<br \/>\n(i) 27<sup>2<\/sup> \u2013 26<sup>2<\/sup> = 27 + 26 = 53<br \/>\n(ii) 118<sup>2<\/sup> \u2013 117<sup>2<\/sup> = 118 + 117 = 235<\/p>\n<p>Question 4.<br \/>\nWrite each of the following numbers as difference of the square of two consecutive natural numbers.<br \/>\n(i) 49<br \/>\n(ii) 75<br \/>\n(iii) 125<br \/>\nSolution:<br \/>\n(i) 49 = 2 \u00d7 24 + 1<br \/>\n49 = 25<sup>2<\/sup> \u2013 24<sup>2<\/sup><br \/>\n(ii) 75 = 2 \u00d7 37 + 1<br \/>\n75 = 38<sup>2<\/sup> \u2013 37<sup>2<\/sup><br \/>\n(iii) 125 = 2 \u00d7 62 + 1<br \/>\n125 = 63<sup>2<\/sup> \u2013 62<sup>2<\/sup><\/p>\n<p>Question 5.<br \/>\nWrite down the following as sum of odd numbers.<br \/>\n(i) 7<sup>2<\/sup><br \/>\n(ii) 9<sup>2<\/sup><br \/>\nSolution:<br \/>\n(i) 7<sup>2<\/sup> = Sum of first 7 odd numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13<br \/>\n(ii) 9<sup>2<\/sup> = Sum of first 9 odd numbers = 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17<\/p>\n<p>Question 6.<br \/>\nExpress the following as the sum of two consecutive integers.<br \/>\n(i) 15<sup>2<\/sup><br \/>\n(ii) 19<sup>2<\/sup><br \/>\nSolution:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998256852_59e2b8accf_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q6\" width=\"374\" height=\"158\" \/><\/p>\n<p>Question 7.<br \/>\nFind the product of the following:<br \/>\n(i) 23 \u00d7 25<br \/>\n(ii) 41 \u00d7 43<br \/>\nSolution:<br \/>\n(i) 23 \u00d7 25 = (24 \u2013 1) (24 + 1) = 24<sup>2<\/sup> \u2013 1 = 576 \u2013 1 = 575<br \/>\n(ii) 41 \u00d7 43 = (42 \u2013 1) (42 + 1) = 42<sup>2<\/sup> \u2013 1 = 1764 \u2013 1 = 1763<\/p>\n<p>Question 8.<br \/>\nFind the squares of:<br \/>\n(i) \\(\\frac { -3 }{ 7 }\\)<br \/>\n(ii) \\(\\frac { -9 }{ 17 }\\)<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998256887_53b2134301_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q8\" width=\"279\" height=\"119\" \/><\/p>\n<p>Question 9.<br \/>\nCheck whether (6, 8, 10) is a Pythagorean triplet.<br \/>\nSolution:<br \/>\n2m, m<sup>2<\/sup> \u2013 1 and m<sup>2<\/sup> + 1 represent the Pythagorean triplet.<br \/>\nLet 2m = 6 \u21d2 m = 3<br \/>\nm<sup>2<\/sup> \u2013 1 = (3)<sup>2<\/sup> \u2013 1 = 9 \u2013 1 = 8<br \/>\nand m<sup>2<\/sup> + 1 = (3)<sup>2<\/sup> + 1 = 9 + 1 = 10<br \/>\nHence (6, 8, 10) is a Pythagorean triplet.<br \/>\nAlternative Method:<br \/>\n(6)<sup>2<\/sup> + (8)<sup>2<\/sup> = 36 + 64 = 100 = (10)<sup>2<\/sup><br \/>\n\u21d2 (6, 8, 10) is a Pythagorean triplet.<\/p>\n<p>Question 10.<br \/>\nUsing property, find the value of the following:<br \/>\n(i) 19<sup>2<\/sup> \u2013 18<sup>2<\/sup><br \/>\n(ii) 23<sup>2<\/sup> \u2013 22<sup>2<\/sup><br \/>\nSolution:<br \/>\n(i) 19<sup>2<\/sup> \u2013 18<sup>2<\/sup> = 19 + 18 = 37<br \/>\n(ii) 23<sup>2<\/sup> \u2013 22<sup>2<\/sup> = 23 + 22 = 45<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Squares_and_Square_Roots_Class_8_Extra_Questions_Short_Answer_Type\"><\/span>Squares and Square Roots Class 8 Extra Questions Short Answer Type<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Question 11.<br \/>\nUsing the prime factorisation method, find which of the following numbers are not perfect squares.<br \/>\n(i) 768<br \/>\n(ii) 1296<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998256952_ae27438ab6_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q11\" width=\"112\" height=\"214\" \/><br \/>\n768 = <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 3<br \/>\nHere, 3 is not in pair.<br \/>\n768 is not a perfect square.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998255998_a64bcdd4c3_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q11.1\" width=\"132\" height=\"195\" \/><br \/>\n1296 = <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">3 \u00d7 3<\/span> \u00d7 <span style=\"text-decoration: underline\">3 \u00d7 3<\/span><br \/>\nHere, there is no number left to make a pair.<br \/>\n1296 is a perfect square.<\/p>\n<p>Question 12.<br \/>\nWhich of the following triplets are Pythagorean?<br \/>\n(i) (14, 48, 50)<br \/>\n(ii) (18, 79, 82)<br \/>\nSolution:<br \/>\nWe know that 2m, m<sup>2<\/sup> \u2013 1 and m<sup>2<\/sup> + 1 make Pythagorean triplets.<br \/>\n(i) For (14, 48, 50),<br \/>\nPut 2m =14 \u21d2 m = 7<br \/>\nm<sup>2<\/sup> \u2013 1 = (7)<sup>2<\/sup> \u2013 1 = 49 \u2013 1 = 48<br \/>\nm<sup>2<\/sup> + 1 = (7)<sup>2<\/sup> + 1 = 49 + 1 = 50<br \/>\nHence (14, 48, 50) is a Pythagorean triplet.<br \/>\n(ii) For (18, 79, 82)<br \/>\nPut 2m = 18 \u21d2 m = 9<br \/>\nm<sup>2<\/sup> \u2013 1 = (9)<sup>2<\/sup> \u2013 1 = 81 \u2013 1 = 80<br \/>\nm<sup>2 <\/sup>+ 1 = (9)<sup>2<\/sup> + 1 = 81 + 1 = 82<br \/>\nHence (18, 79, 82) is not a Pythagorean triplet.<\/p>\n<p>Question 13.<br \/>\nFind the square root of the following using successive subtraction of odd numbers starting from 1.<br \/>\n(i) 169<br \/>\n(ii) 81<br \/>\n(iii) 225<br \/>\nSolution:<br \/>\n(i) 169 \u2013 1 = 168, 168 \u2013 3 = 165, 165 \u2013 5 = 160, 160 \u2013 7 = 153, 153 \u2013 9 = 144, 144 \u2013 11 = 133, 133 \u2013 13 = 120, 120 \u2013 15 = 105, 105 \u2013 17 = 88, 88 \u2013 19 = 69,<br \/>\n69 \u2013 21 = 48, 48 \u2013 23 = 25, 25 \u2013 25 = 0<br \/>\nWe have subtracted odd numbers 13 times to get 0.<br \/>\n\u221a169 = 13<br \/>\n(ii) 81 \u2013 1 = 80, 80 \u2013 3 = 77, 77 \u2013 5 = 72, 72 \u2013 7 = 65, 65 \u2013 9 = 56, 56 \u2013 11 = 45, 45 \u2013 13 = 32, 32 \u2013 15 = 17, 17 \u2013 17 = 0<br \/>\nWe have subtracted 9 times to get 0.<br \/>\n\u221a81 = 9<br \/>\n(iii) 225 \u2013 1 = 224, 224 \u2013 3 = 221, 221 \u2013 5 = 216, 216 \u2013 7 = 209, 209 \u2013 9 = 200, 200 \u2013 11 = 189, 189 \u2013 13 = 176, 176 \u2013 15 = 161, 161 \u2013 17 = 144, 144 \u2013 19 = 125,<br \/>\n125 \u2013 21 = 104, 104 \u2013 23 = 81, 81 \u2013 25 = 56, 56 \u2013 27 = 29, 29 \u2013 29 = 0<br \/>\nWe have subtracted 15 times to get 0.<br \/>\n\u221a225 = 15<\/p>\n<p>Question 14.<br \/>\nFind the square rootofthe following using prime factorisation<br \/>\n(i) 441<br \/>\n(ii) 2025<br \/>\n(iii) 7056<br \/>\n(iv) 4096<br \/>\nSolution:<br \/>\n(i) 441 = <span style=\"text-decoration: underline\">3 \u00d7 3<\/span> \u00d7 <span style=\"text-decoration: underline\">7 \u00d7 7<\/span><br \/>\n\u221a441 = 3 \u00d7 7 = 21<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998297141_5e79b6f864_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q14\" width=\"102\" height=\"121\" \/><br \/>\n(ii) 2025 = <span style=\"text-decoration: underline\">3 \u00d7 3<\/span> \u00d7 <span style=\"text-decoration: underline\">3 \u00d7 3<\/span> \u00d7 <span style=\"text-decoration: underline\">5 \u00d7 5<\/span><br \/>\n\u221a2025 = 3 \u00d7 3 \u00d7 5 = 45<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998297191_968cf16e85_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q14.1\" width=\"102\" height=\"167\" \/><br \/>\n(iii) 7056 = <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">3 \u00d7 3<\/span> \u00d7 <span style=\"text-decoration: underline\">7 \u00d7 7<\/span><br \/>\n\u221a7056 = 2 \u00d7 2 \u00d7 3 \u00d7 7 = 84<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998256098_8a7b7729f6_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q14.2\" width=\"99\" height=\"192\" \/><br \/>\n(iv) 4096 = <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 <span style=\"text-decoration: underline\">2 \u00d7 2<\/span><br \/>\n\u221a4096 = 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 2 = 64<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998297261_a7311a0769_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q14.3\" width=\"106\" height=\"281\" \/><\/p>\n<p>Question 15.<br \/>\nFind the least square number which is divisible by each of the number 4, 8 and 12.<br \/>\nSolution:<br \/>\nLCM of 4, 8, 12 is the least number divisible by each of them.<br \/>\nLCM of 4, 8 and 12 = 24<br \/>\n24 = <span style=\"text-decoration: underline\">2 \u00d7 2<\/span> \u00d7 2 \u00d7 3<br \/>\nTo make it perfect square multiply 24 by the product of unpaired numbers, i.e., 2 \u00d7 3 = 6<br \/>\nRequired number = 24 \u00d7 6 = 144<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998256193_053dd2f069_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q15\" width=\"129\" height=\"123\" \/><\/p>\n<p>Question 16.<br \/>\nFind the square roots of the following decimal numbers<br \/>\n(i) 1056.25<br \/>\n(ii) 10020.01<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998297396_e7a3106c4d_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q16\" width=\"199\" height=\"221\" \/><br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998256323_753aa274d7_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q16.1\" width=\"246\" height=\"184\" \/><\/p>\n<p>Question 17.<br \/>\nWhat is the least number that must be subtracted from 3793 so as to get a perfect square? Also, find the square root of the number so obtained.<br \/>\nSolution:<br \/>\nFirst, we find the square root of 3793 by division method.<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998257377_073731f7b9_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q17\" width=\"114\" height=\"149\" \/><br \/>\nHere, we get a remainder 72<br \/>\n61<sup>2<\/sup> &lt; 3793<br \/>\nRequired perfect square number = 3793 \u2013 72 = 3721 and \u221a3721 = 61<\/p>\n<p>Question 18.<br \/>\nFill in the blanks:<br \/>\n(\u0430) The perfect square number between 60 and 70 is \u2026\u2026\u2026\u2026<br \/>\n(b) The square root of 361 ends with digit \u2026\u2026\u2026\u2026..<br \/>\n(c) The sum of first n odd numbers is \u2026\u2026\u2026\u2026<br \/>\n(d) The number of digits in the square root of 4096 is \u2026\u2026\u2026..<br \/>\n(e) If (-3)<sup>2<\/sup> = 9, then the square root of 9 is \u2026\u2026\u2026.<br \/>\n(f) Number of digits in the square root of 1002001 is \u2026\u2026\u2026\u2026<br \/>\n(g) Square root of \\(\\frac { 36 }{ 625 }\\) is \u2026\u2026\u2026..<br \/>\n(h) The value of \u221a(63 \u00d7 28) = \u2026\u2026\u2026\u2026<br \/>\nSolution:<br \/>\n(a) 64<br \/>\n(b) 9<br \/>\n(c) n<sup>2<\/sup><br \/>\n(d) 2<br \/>\n(e) \u00b13<br \/>\n(f) 4<br \/>\n(g) \\(\\frac { 6 }{ 25 }\\)<br \/>\n(h) 42<\/p>\n<p>Question 19.<br \/>\nSimplify: \u221a900 + \u221a0.09 + \u221a0.000009<br \/>\nSolution:<br \/>\nWe know that \u221a(ab) = \u221aa \u00d7 \u221ab<br \/>\n\u221a900 = \u221a(9 \u00d7 100) = \u221a9 \u00d7 \u221a100 = 3 \u00d7 10 = 30<br \/>\n\u221a0.09 = \u221a(0.3 \u00d7 0.3) = 0.3<br \/>\n\u221a0.000009 = \u221a(0.003 \u00d7 0.003) = 0.003<br \/>\n\u221a900 + \u221a0.09 + \u221a0.000009 = 30 + 0.3 + 0.003 = 30.303<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Squares_and_Square_Roots_Class_8_Extra_Questions_Higher_Order_Thinking_Skills_HOTS\"><\/span>Squares and Square Roots Class 8 Extra Questions Higher Order Thinking Skills (HOTS)<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Question 20.<br \/>\nFind the value of x if<br \/>\n\\(\\sqrt { 1369 } +\\sqrt { 0.0615+x } =37.25\\)<br \/>\nSolution:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998256358_a39f342630_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q20\" width=\"318\" height=\"428\" \/><\/p>\n<p>Question 21.<br \/>\nSimplify:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998296956_386f0d1f2b_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q21\" width=\"245\" height=\"61\" \/><br \/>\nSolution:<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998297526_faaeac85d0_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q21.1\" width=\"370\" height=\"381\" \/><\/p>\n<p>Question 22.<br \/>\nA ladder 10 m long rests against a vertical wall. If the foot of the ladder is 6 m away from the wall and the ladder just reaches the top of the wall, how high is the wall? (NCERT Exemplar)<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998256767_43966a19e3_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q22\" width=\"176\" height=\"132\" \/><br \/>\nSolution:<br \/>\nLet AC be the ladder.<br \/>\nTherefore, AC = 10 m<br \/>\nLet BC be the distance between the foot of the ladder and the wall.<br \/>\nTherefore, BC = 6 m<br \/>\n\u2206ABC forms a right-angled triangle, right angled at B.<br \/>\nBy Pythagoras theorem,<br \/>\nAC<sup>2<\/sup> = AB<sup>2<\/sup> + BC<sup>2<\/sup><br \/>\n10<sup>2 <\/sup>= AB<sup>2<\/sup> + 6<sup>2<\/sup><br \/>\nor AB<sup>2<\/sup> = 10<sup>2<\/sup> \u2013 6<sup>2<\/sup> = 100 \u2013 36 = 64<br \/>\nor AB = \u221a64 = 8m<br \/>\nHence, the wall is 8 m high.<\/p>\n<p>Question 23.<br \/>\nFind the length of a diagonal of a rectangle with dimensions 20 m by 15 m. (NCERT Exemplar)<br \/>\nSolution:<br \/>\nUsing Pythagoras theorem, we have Length of diagonal of the rectangle = \\(\\sqrt { { l }^{ 2 }+{ b }^{ 2 } }\\) units<br \/>\n<img loading=\"lazy\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/47998256732_355f9cf52c_o.png\" alt=\"Squares and Square Roots NCERT Extra Questions for Class 8 Maths Q23\" width=\"337\" height=\"142\" \/><br \/>\nHence, the length of the diagonal is 25 m.<\/p>\n<p>Question 24.<br \/>\nThe area of a rectangular field whose length is twice its breadth is 2450 m2. Find the perimeter of the field.<br \/>\nSolution:<br \/>\nLet the breadth of the field be x metres. The length of the field 2x metres.<br \/>\nTherefore, area of the rectangular field = length \u00d7 breadth = (2x)(x) = (2x<sup>2<\/sup>) m<sup>2<\/sup><br \/>\nGiven that area is 2450 m<sup>2<\/sup>.<br \/>\nTherefore, 2x<sup>2<\/sup> = 2450<br \/>\n\u21d2 x<sup>2<\/sup> = 1225<br \/>\n\u21d2 x = \u221a1225 or x = 35 m<br \/>\nHence, breadth = 35 m<br \/>\nand length = 35 \u00d7 2 = 70 m<br \/>\nPerimeter of the field = 2 (l + b ) = 2(70 + 35) m = 2 \u00d7 105 m = 210 m.<\/p>\n<p><img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-01.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-01\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-02.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-02\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-03.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-03\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-04.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-04\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-05.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-05\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-06.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-06\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-07.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-07\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-08.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-08\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-09.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-09\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-10.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-10\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-11.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-11\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-12.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-12\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-13.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-13\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-14.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-14\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-15.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-15\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-16.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-16\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-17.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-17\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-18.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-18\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-19.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-19\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-20.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-20\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-21.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-21\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-22.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-22\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-23.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-23\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-24.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-24\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-25.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-25\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-26.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-26\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-27.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-27\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-28.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-28\" \/><br \/>\n<img src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2021\/12\/squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-29.png\" alt=\"squares-and-square-roots-ncert-extra-questions-for-class-8-maths-chapter-6-29\" \/><\/p>\n<h4><\/h4>\n","protected":false},"excerpt":{"rendered":"<p>Squares and Square Roots Class 8 Extra Questions Maths Chapter 6 Extra Questions for Class 8 Maths Chapter 6 Squares [&hellip;]<\/p>\n","protected":false},"author":7,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"","_yoast_wpseo_title":"","_yoast_wpseo_metadesc":"Get Squares and Square Roots Class 8 Extra Questions Maths Chapter 6 on Infinity Learn.","custom_permalink":"study-material\/cbse-notes\/class-8\/maths\/squares-and-square-roots-class-8-extra-questions-maths-chapter-6\/"},"categories":[92,93,13,21],"tags":[],"table_tags":[],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v17.9 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Squares and Square Roots Class 8 Extra Questions Maths Chapter 6 - Infinity Learn by Sri Chaitanya<\/title>\n<meta name=\"description\" content=\"Get Squares and Square Roots Class 8 Extra Questions Maths Chapter 6 on Infinity Learn.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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