{"id":44977,"date":"2023-04-24T13:22:10","date_gmt":"2023-04-24T07:52:10","guid":{"rendered":"https:\/\/icsesolutions.com\/?p=44977"},"modified":"2023-04-25T10:21:46","modified_gmt":"2023-04-25T04:51:46","slug":"ml-aggarwal-class-8-solutions-for-icse-maths-chapter-4-ex-4-2","status":"publish","type":"post","link":"https:\/\/icsesolutions.com\/ml-aggarwal-class-8-solutions-for-icse-maths-chapter-4-ex-4-2\/","title":{"rendered":"ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2"},"content":{"rendered":"
Question 1.
\nFind the cube root of each of the following numbers by prime factorisation:
\n(i) 12167
\n(ii) 35937
\n(iii) 42875
\n(iv) 21952
\n(v) 373248
\n(vi) 32768
\n(vii) 262144
\n(viii) 157464
\nSolution:
\n
\n
\n
\n
\n
\n
\n<\/p>\n
Question 2. (ii) 59319 (iii) 85184 (iv) 148877 Question 3. Question 4. Question 5. Question 6. Question 7. Question 8. Question 9. Question 10. Question 11. Question 12. ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2 Question 1. Find the cube root of each of the following numbers by prime factorisation: (i) 12167 (ii) 35937 (iii) 42875 (iv) 21952 (v) 373248 (vi) 32768 (vii) 262144 (viii) 157464 Solution: Question 2. Find the cube root of …<\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[3034],"tags":[],"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts\/44977"}],"collection":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/comments?post=44977"}],"version-history":[{"count":1,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts\/44977\/revisions"}],"predecessor-version":[{"id":159194,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/posts\/44977\/revisions\/159194"}],"wp:attachment":[{"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/media?parent=44977"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/categories?post=44977"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/icsesolutions.com\/wp-json\/wp\/v2\/tags?post=44977"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\nFind the cube root of each of the following cube numbers through estimation.
\n(i) 19683
\n(ii) 59319
\n(iii) 85184
\n(iv) 148877
\nSolution:
\n(i) 19683
\nGrouping in 3’s from right to left, 19,683
\nIn the first group 683, the unit digit is 3
\n\u2234 The cube root will be 7
\nand in the second group, 19
\nCubing 23<\/sup> = 8 and 33<\/sup> = 27
\n\u2234 8 < 14 < 21
\n\u2234 The tens digit of the cube will be 2
\n\u2234 Cube root of 19683 = 27<\/p>\n
\nGrouping in 3’s, from right to left. 59,319
\nIn first group, 319 unit digit is 9
\n\u2234 Unit digit of its cube root will be 9
\nand group 2nd, 59
\n33<\/sup> = 27, 43<\/sup> = 64
\n27 < 59 < 64
\n\u2234 Ten’s digit will be 3
\n\u2234 Cube root = 39<\/p>\n
\nGrouping in 3’s from right to left 85,184
\nIn group first 184, the unit digit is 4
\n\u2234 Unit digit of its cube root will be 4 and in group 2nd 85,
\n43<\/sup> = 64 and 53<\/sup> = 125
\n64 < 85 < 125
\n\u2234 Ten’s digit of cube root will be 4
\n\u2234 Cube root = 44<\/p>\n
\nGrouping in 3’s, from right to left 148,877
\nIn the first group 877, unit digit is 7
\n\u2234 The unit digit of cube root will be 3
\nand in group 2nd 148
\n53<\/sup> = 125, 63<\/sup> = 216
\n125 < 148 < 216
\n\u2234 Ten’s digit of cube root will be 5
\n\u2234 Cube root = 53<\/p>\n
\nFind the cube root of each of the following numbers:
\n
\nSolution:
\n
\n
\n
\n<\/a><\/p>\n
\nEvaluate the following:
\n(i) \\(\\sqrt[3]{512 \\times 729}\\)
\n(ii) \\(\\sqrt[3]{(-1331) \\times(3375)}\\)
\nSolution:
\n
\n<\/p>\n
\nFind the cube root of the following decimal numbers:
\n(i) 0.003375
\n(ii) 19.683
\nSolution:
\n
\n
\n<\/p>\n
\nEvaluate: \\(\\sqrt[3]{27}+\\sqrt[3]{0.008}+\\sqrt[3]{0.064}\\)
\nSolution:
\n<\/p>\n
\nMultiply 6561 by the smallest number so that product is a perfect cube. Also, find the cube root of the product.
\nSolution:
\n6561
\nFactorising, we get
\n
\n6561 = 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3
\nGrouping of the equal factors in 3’s,
\nwe see that 3 \u00d7 3 is left ungrouped in 3’s.
\nIn order to complete it in triplet, we should multiply it by 3.
\nHence, required smallest number = 3
\nand cube root of the product = 3 \u00d7 3 \u00d7 3 = 27<\/p>\n
\nDivide the number 8748 by the smallest number so that the quotient is a perfect cube. Also, find the cube root of the quotient.
\nSolution:
\n8748
\nFactorising, we get
\n
\n8748 = 2 \u00d7 2 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3 \u00d7 3
\nGrouping of the equal factor in 3’s
\nwe get that 2 \u00d7 2 \u00d7 3 is left without grouping.
\nSo, dividing 8748 by 12, we get 729
\nwhose cube root is 3 \u00d7 3 = 9<\/p>\n
\nThe volume of a cubical box is 21952 m3<\/sup>. Find the length of the side of the box.
\nSolution:
\nThe volume of a cubical box 21952 m2<\/sup>
\n
\n= \\(\\sqrt[3]{2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 2 \\times 7 \\times 7 \\times 7} \\mathrm{m}\\)
\n= 2 \u00d7 2 \u00d7 7 = 28 m<\/p>\n
\nThree numbers are in the ratio 3 : 4 : 5. If their product is 480, find the numbers.
\nSolution:
\nThree numbers are in the ratio 3:4:5
\nand their product = 480
\nLet numbers be 3x, Ax, 5x, then
\n3x \u00d7 4x \u00d7 5x = 480 \u21d2 60 \u00d7 3 = 480
\n\u21d2 x3<\/sup> = \\(\\frac{480}{60}\\) = 8 = (2)3<\/sup>
\n\u2234 x = 2
\n\u2234 Number are 2 \u00d7 3, 2 \u00d7 4, 2 \u00d7 5
\n= 6, 8 and 10<\/p>\n
\nTw’o numbers are in the ratio 4 : 5. If difference of their cubes is 61, find the numbers.
\nSolution:
\nTwo numbers are in the ratio = 4 : 5
\nDifference between their cubes = 61
\nLet the numbers be 4x, 5x
\n\u2234 (5x)3<\/sup> – (4x)3<\/sup> = 61
\n125x3<\/sup> – 64x3<\/sup> = 61 \u21d2 61x3<\/sup> = 61
\n\u21d2 x3<\/sup> = 1 = (1)3<\/sup>
\n\u2234 x = 1
\n\u2234 Numbers are 4x = 4 \u00d7 1 = 4 and 5 \u00d7 1 = 5
\nHence numbers are = 4, 5<\/p>\n
\nDifference of two perfect cubes is 387. If the cube root of the greater of two numbers is 8, find the cube root of the smaller number.
\nSolution:
\nDifference in two cubes = 387
\nCube root of the greater number = 8
\n\u2234 Greater number = (8)3<\/sup> = 8 \u00d7 8 \u00d7 8 = 512
\nHence, second number = 512 – 387 = 125
\nand cube root of 125 = \\(\\sqrt[3]{125}\\)
\n= \\(\\sqrt[3]{5 \\times 5 \\times 5}\\) = 5<\/p>\nML Aggarwal Class 8 Solutions for ICSE Maths<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"