{"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":"

ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 4 Cubes and Cube Roots Ex 4.2<\/h2>\n

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\"ML
\n\"ML
\n\"ML
\n\"ML
\n\"ML
\n\"ML
\n\"ML<\/p>\n

Question 2.
\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

(ii) 59319
\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

(iii) 85184
\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

(iv) 148877
\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

Question 3.
\nFind the cube root of each of the following numbers:
\n\"ML
\nSolution:
\n\"ML
\n\"ML
\n\"ML
\n\"ML<\/a><\/p>\n

Question 4.
\nEvaluate the following:
\n(i) \\(\\sqrt[3]{512 \\times 729}\\)
\n(ii) \\(\\sqrt[3]{(-1331) \\times(3375)}\\)
\nSolution:
\n\"ML
\n\"ML<\/p>\n

Question 5.
\nFind the cube root of the following decimal numbers:
\n(i) 0.003375
\n(ii) 19.683
\nSolution:
\n\"ML
\n\"ML
\n\"ML<\/p>\n

Question 6.
\nEvaluate: \\(\\sqrt[3]{27}+\\sqrt[3]{0.008}+\\sqrt[3]{0.064}\\)
\nSolution:
\n\"ML<\/p>\n

Question 7.
\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\"ML
\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

Question 8.
\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\"ML
\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

Question 9.
\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\"ML
\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

Question 10.
\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

Question 11.
\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

Question 12.
\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>\n

ML Aggarwal Class 8 Solutions for ICSE Maths<\/a><\/h4>\n","protected":false},"excerpt":{"rendered":"

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}]}}