{"id":27476,"date":"2023-04-06T14:29:35","date_gmt":"2023-04-06T08:59:35","guid":{"rendered":"https:\/\/ncertsolutions.guru\/?p=27476"},"modified":"2023-04-06T17:11:32","modified_gmt":"2023-04-06T11:41:32","slug":"ncert-solutions-for-class-8-maths-chapter-7-ex-7-1","status":"publish","type":"post","link":"https:\/\/ncertsolutions.guru\/ncert-solutions-for-class-8-maths-chapter-7-ex-7-1\/","title":{"rendered":"NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.1"},"content":{"rendered":"

These NCERT Solutions for Class 8 Maths<\/a> Chapter 7 Cube and Cube Roots Ex 7.1 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 7.1<\/h2>\n

Question 1.
\nWhich of the following numbers are not perfect cubes?
\n(i) 216
\n(ii) 128
\n(iii) 1000
\n(iv) 100
\n(v) 46656
\nSolution:
\n(i) 216
\n216 = 23<\/sup> \u00d7 33<\/sup>
\nEach prime factors appear in triplets, so 216 is a perfect cube.
\n\"NCERT<\/p>\n

(ii) 128
\n128 = 23<\/sup> \u00d7 23<\/sup> \u00d7 2
\n2 remains after grouping in triplets, so 128 is not a perfect cube.
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

(iii) 1000
\n1000 = 23<\/sup> \u00d7 53<\/sup>
\nEach prime factor appears in triplets so 1000 is a perfect cube.
\n\"NCERT<\/p>\n

(iv) 100
\n100 = 22<\/sup> \u00d7 52<\/sup>
\nAs we do not get any triplets, So 100 is not a perfect cube.
\n\"NCERT<\/p>\n

(v) 46656
\n46656 = 23<\/sup> \u00d7 23<\/sup> \u00d7 33<\/sup> \u00d7 33<\/sup>
\nEach prime factor appears in triplets, so 46656 is a perfect cube.
\n\"NCERT<\/p>\n

Question 2.
\nFind the smallest number by which each of the following numbers must be multiplied to obtain a perfect cube.
\n(i) 243
\n(ii) 256
\n(iii) 72
\n(iv) 675
\n(v) 100
\nSolution:
\n(i) 243
\n243 = 33<\/sup> \u00d7 32<\/sup>
\nOn grouping the factors in triplets, the prime factor 3 does not appear in a group of three.
\nTo make it a perfect cube, we need one more 3.
\nThe number 243 should be multiplied by 3 to get a perfect cube.
\n\"NCERT<\/p>\n

(ii) 256
\n256 = 23<\/sup> \u00d7 23<\/sup> \u00d7 22<\/sup>
\nOn grouping the factors in triplets, the prime factor 2 does not appears in a group of three.
\nTo make it a perfect cube, we need one more 2.
\nThe number 256 should be multiplied by 2 to get a perfect cube.
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

(iii) 72
\n72 = 23<\/sup> \u00d7 32<\/sup>
\nOn grouping, the factors in triplets the prime factor 3 does not appear in a group of 3.
\nTo make it a perfect cube, we multiply it by 3.
\nThe number 72 should be multiplied by 3 to get a perfect cube.
\n\"NCERT<\/p>\n

(iv) 675
\n675 = 33<\/sup> \u00d7 52<\/sup>
\nOn grouping the factors in triplets, the prime factor 5 does not appear in a group of three.
\nTo make it a perfect cube, we multiply it by 5.
\nThe number 675 should be multiplied by 5 to get a perfect cube.
\n\"NCERT<\/p>\n

(v) 100
\n100 = 22<\/sup> \u00d7 52<\/sup>
\nOn grouping the factors in triplets, the prime factors 2 and 5 do not appear in a group of three.
\nTo make it a perfect cube we need one 2 and one 5 (2 \u00d7 5 = 10)
\nThe number 100 should be multiplied by 10 to get a perfect cube.
\n\"NCERT<\/p>\n

Question 3.
\nFind the smallest number by which each of the following numbers must be divided to obtain a perfect cube.
\n(i) 81
\n(ii) 128
\n(iii) 135
\n(iv) 192
\n(v) 704
\nSolution:
\n(i) 81
\n81 = 33<\/sup> \u00d7 3
\nOn grouping the factors in triplets, we find that three is no triplet of 3.
\nTo make it a perfect cube, we divide it by 3.
\n\"NCERT<\/p>\n

(ii) 128
\n128 = 23<\/sup> \u00d7 23<\/sup> \u00d7 2
\nOn grouping the factors in triplets, we find that there is no triplet of 2.
\nTo make it a perfect cube, we divide it by 2.
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

(iii) 135
\n135 = 33<\/sup> \u00d7 5
\nOn grouping the factors in triplets, the prime factor 5 does not appear in a group of three.
\nTo make it a perfect cube, 135 should be divided by 5.
\n\"NCERT<\/p>\n

(iv) 192
\n192 = 23<\/sup> \u00d7 23<\/sup> \u00d7 3
\nOn grouping the factors in triplets, the prime factor 3 does not appear in a group of three.
\nTo make it a perfect cube, 192 should be divided by 3.
\n\"NCERT<\/p>\n

(v) 704
\n704 = 23<\/sup> \u00d7 23<\/sup> \u00d7 11
\nOn grouping the factors in triplets, the prime factor 11 does not appear in a group of three.
\nTo make it a perfect cube, 704 should be divided by 11.
\n\"NCERT<\/p>\n

\"NCERT<\/p>\n

Question 4.
\nParikshit makes a cuboid of plasticine on sides 5 cm, 2 cm, 5 cm. How many such cuboids will he need to form a cube?
\nSolution:
\nSides of the cuboid are 5 cm, 2 cm, and 5 cm
\nVolume of the cuboid = 5 cm \u00d7 2 cm \u00d7 5 cm
\nTo form it as a cube, its dimension should be in the group of triplets.
\nSince there is only one 2 and only two 5 in the prime factorization.
\nWe need 2 \u00d7 2 \u00d7 5 = 20 such cuboids to make a cube.<\/p>\n","protected":false},"excerpt":{"rendered":"

These NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.1 Questions and Answers are prepared by our highly skilled subject experts. NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Exercise 7.1 Question 1. Which of the following numbers are not perfect cubes? (i) 216 (ii) 128 …<\/p>\n

NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.1<\/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 7.1 - 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-7-1\/\" \/>\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 7.1 - NCERT Solutions\" \/>\n<meta property=\"og:description\" content=\"These NCERT Solutions for Class 8 Maths Chapter 7 Cube and Cube Roots Ex 7.1 Questions and Answers are prepared by our highly skilled subject experts. 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