{"id":27503,"date":"2021-06-30T17:49:21","date_gmt":"2021-06-30T12:19:21","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=27503"},"modified":"2021-06-30T17:53:18","modified_gmt":"2021-06-30T12:23:18","slug":"ncert-solutions-for-class-8-maths-chapter-7-ex-7-2","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-8-maths-chapter-7-ex-7-2\/","title":{"rendered":"NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.2"},"content":{"rendered":"

These NCERT Solutions for Class 8 Maths<\/a> Chapter 7 Cube and Cube Roots Ex 7.2 Questions and Answers are prepared by our highly skilled subject experts.<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Exercise 7.2<\/h2>\n

Question 1.
\nFind the cube root of each of the following numbers by prime factorisation method.
\n(i) 64
\n(ii) 512
\n(iii) 10648
\n(iv) 27000
\n(v) 15625
\n(vi) 13824
\n(vii) 110592
\n(viii) 46656
\n(ix) 175616
\n(x) 91125
\nSolution:
\n(i) 64
\nOn grouping the factors in triplets, we get
\n64 = 23<\/sup> \u00d7 23<\/sup>
\n64 = (2 \u00d7 2)3<\/sup> = 43<\/sup>
\n\\(\\sqrt[3]{64}\\) = 4
\n\"NCERT<\/p>\n

(ii) 512
\nOn grouping the factors in triplets, we get
\n512 = 23<\/sup> \u00d7 23<\/sup> \u00d7 23<\/sup>
\n= (2 \u00d7 2 \u00d7 2)3<\/sup>
\n= 83<\/sup>
\n\\(\\sqrt[3]{512}\\) = 8
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

(iii) 10648
\nOn grouping the factors in triplets, we get
\n10648 = 23<\/sup> \u00d7 113<\/sup>
\n= (2 \u00d7 11)3<\/sup>
\n= 223<\/sup>
\n\\(\\sqrt[3]{10648}\\) = 22
\n\"NCERT<\/p>\n

(iv) 27000
\nOn grouping the factors in triplets, we get
\n27000 = 23<\/sup> \u00d7 33<\/sup> \u00d7 53<\/sup>
\n= (2 \u00d7 3 \u00d7 5)3<\/sup>
\n= 303<\/sup>
\n\\(\\sqrt[3]{27000}\\) = 30
\n\"NCERT<\/p>\n

(v) 15625
\nOn grouping the factors in triplets, we get
\n15625 = 53<\/sup> \u00d7 53<\/sup>
\n= (5 \u00d7 5)3<\/sup>
\n= 253<\/sup>
\n\\(\\sqrt[3]{15625}\\) = 25
\n\"NCERT<\/p>\n

(vi) 13824
\nOn grouping the factors in triplets, we get
\n13824 = 23<\/sup> \u00d7 23<\/sup> \u00d7 23<\/sup> \u00d7 33<\/sup>
\n= (2 \u00d7 2 \u00d7 2 \u00d7 3)3<\/sup>
\n= 243<\/sup>
\n\\(\\sqrt[3]{13824}\\) = 24
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

(vii) 110592
\nOn grouping the factors in triplets, we get
\n110592 = 23<\/sup> \u00d7 23<\/sup> \u00d7 23<\/sup> \u00d7 23<\/sup> \u00d7 33<\/sup>
\n= (2 \u00d7 2 \u00d7 2 \u00d7 2 \u00d7 3)3<\/sup>
\n= 483<\/sup>
\n\\(\\sqrt[3]{110592}\\) = 48
\n\"NCERT<\/p>\n

(viii) 46656
\nOn grouping the factors in triplets, we get
\n46656 = 23<\/sup> \u00d7 23<\/sup> \u00d7 33<\/sup> \u00d7 33<\/sup>
\n= (2 \u00d7 2 \u00d7 3 \u00d7 3)3<\/sup>
\n= 363<\/sup>
\n\\(\\sqrt[3]{46656}\\) = 36
\n\"NCERT<\/p>\n

(ix) 175616
\nOn grouping the factors in triplets, we get
\n175616 = 23<\/sup> \u00d7 23<\/sup> \u00d7 23<\/sup> \u00d7 73<\/sup>
\n= (2 \u00d7 2 \u00d7 2 \u00d7 7)3<\/sup>
\n= 563<\/sup>
\n\\(\\sqrt[3]{175616}\\) = 56
\n\"NCERT<\/p>\n

(x) 91125
\nOn grouping the factors in triplets, we get
\n91125 = 33<\/sup> \u00d7 33<\/sup> \u00d7 53<\/sup>
\n= (3 \u00d7 3 \u00d7 5)3<\/sup>
\n= 453<\/sup>
\n\\(\\sqrt[3]{91125}\\) = 45
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 2.
\nState true or false.
\n(i) Cube of any odd number is even.
\n(ii) A perfect cube does not end with two zeros.
\n(iii) If the square of a number ends with 5, then its cube ends with 25.
\n(iv) There is no perfect cube which ends with 8.
\n(v) The cube of a two-digit number may be a three-digit number.
\n(vi) The cube of a two-digit number may have seven or more digits.
\n(vii) The cube of a single-digit number may be a single-digit number.
\nSolution:
\n(i) False
\n(ii) True
\n(iii) False [152<\/sup> = 225; 153<\/sup> = 3375]
\n(iv) False [123<\/sup> = 1728]
\n(v) False [103<\/sup> = 1000]
\n(vi) False [993<\/sup> = 970299]
\n(vii) True [23<\/sup> = 8]<\/p>\n

Question 3.
\nYou are told that 1,331 is a perfect cube. Can you guess without factorization what is its cube root? Similarly, guess the cube roots of 4913, 12167, 32768.
\nSolution:
\n(i) Separating the given number 1331 into two groups.
\n1 and 331
\n331 ends in 1
\nunit digit of the cube root = 1
\nTens digit of the cube root = 1
\n\\(\\sqrt[3]{1331}\\) = 11<\/p>\n

\"NCERT<\/p>\n

(ii) Cube root of 4913
\nSeparating the given number 4913 in two groups i.e. 4 and 913
\nIn this case, 913 has three-digit and 4 has only one digit
\nThe digit 3 is at its own place. We take the one\u2019s place of the required cube root as 7.
\nTake the other group i.e. 4, a cube of 1 is 1, and a cube of 2 is 8. 4 lies between 1 and 8.
\nThe smaller number among 1 and 2 is 1
\nThe one place of 1 is 1 itself.
\nTake 1 as ten\u2019s place of the cube root of 4913.
\n\\(\\sqrt[3]{4913}\\) = 17<\/p>\n

(iii) Cube root of 12167
\nSeparating 12167 in two groups i.e. 12 and 167
\nThe digit 7 is at its one’s place. We take the one\u2019s place of required cube root as 3.
\nThe unit digit of the cube root = 3
\nTake the other group i.e. 12 Cube of 2 is 8 and cube of 3 is 27. 12 lies between 8 and 27
\nThe smaller among 2 and 3 is 2
\nThe one place is 2 itself.
\nTake 2 as ten\u2019s place of the cube root of 12167.
\n\\(\\sqrt[3]{12167}\\) = 23<\/p>\n

\"NCERT<\/p>\n

(iv) Cube root of 32768
\nSeparating 32768 in two groups i.e. 32 and 768
\nTake 768
\nThe digit 8 is at its one\u2019s place so, the one\u2019s place of the required cube root is 2.
\nTake the other group i.e. 32
\nThe cube of 3 is 27 and the cube of 4 is 64.
\n32 lies between 27 and 64.
\nThe smaller number between 3 and 4 is 3
\nTake 3 as ten\u2019s place of the cube root of 32768
\n\\(\\sqrt[3]{32768}\\) = 32<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.2 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Exercise 7.2 Question 1. Find the cube root of each of the following numbers by prime factorisation …<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.2<\/span> Read More »<\/a><\/p>\n","protected":false},"author":9,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[7],"tags":[],"yoast_head":"\nNCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.2 - NCERT Solutions<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-8-maths-chapter-7-ex-7-2\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.2 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.2 Questions and Answers are prepared by our highly skilled subject experts. 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NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Exercise 7.2 Question 1. 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