{"id":95387,"date":"2019-10-04T10:57:28","date_gmt":"2019-10-04T05:27:28","guid":{"rendered":"https:\/\/www.cbselabs.com\/?p=95387"},"modified":"2021-09-18T15:16:37","modified_gmt":"2021-09-18T09:46:37","slug":"ncert-solutions-for-class-8-maths-chapter-7-cubes-and-cube-roots","status":"publish","type":"post","link":"https:\/\/www.cbselabs.com\/ncert-solutions-for-class-8-maths-chapter-7-cubes-and-cube-roots\/","title":{"rendered":"NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots"},"content":{"rendered":"
NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.1<\/strong><\/p>\n Ex 7.1 Class 8 Maths Question 1. Ex 7.1 Class 8 Maths\u00a0Question 2. Ex 7.1 Class 8 Maths\u00a0Question 3. Ex 7.1 Class 8 Maths\u00a0Question 4. <\/p>\n <\/p>\n <\/p>\n NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Class 8 Maths Cubes and Cube Roots Exercise 7.1 Class 8 Maths Cubes and Cube Roots Exercise 7.2 Cubes and Cube Roots Class 8 Extra Questions NCERT Solutions for Class 8 Maths Chapter 7 Cubes and Cube Roots Exercise 7.1 Ex 7.1 Class …<\/p>\n","protected":false},"author":27,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[2],"tags":[],"yoast_head":"\n
\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) Prime factorisation of 216 is:
\n216 = 2 \u00d7 2 \u00d7 2<\/span> \u00d7 3 \u00d7 3 \u00d7 3<\/span>
\nIn the above factorisation, 2 and 3 have formed a group of three.
\nThus, 216 is a perfect cube.
\n
\n(ii) Prime factorisation of 128 is:
\n128 = 2 \u00d7 2 \u00d7 2<\/span> \u00d7 2 \u00d7 2 \u00d7 2<\/span> \u00d7 2
\nHere, 2 is left without making a group of three.
\nThus 128 is not a perfect cube.
\n
\n(iii) Prime factorisation of 1000, is:
\n1000 = 2 \u00d7 2 \u00d7 2<\/span> \u00d7 5 \u00d7 5 \u00d7 5<\/span>
\nHere, no number is left for making a group of three.
\nThus, 1000 is a perfect cube.
\n
\n(iv) Prime factorisation of 100, is:
\n100 = 2 \u00d7 2<\/span> \u00d7 5 \u00d7 5<\/span>
\nHere 2 and 5 have not formed a group of three.
\nThus, 100 is not a perfect cube.
\n
\n(v) Prime factorisation of 46656 is:
\n46656 = 2 \u00d7 2 \u00d7 2<\/span> \u00d7 2 \u00d7 2 \u00d7 2<\/span> \u00d7 3 \u00d7 3 \u00d7 3<\/span> \u00d7 3 \u00d7 3 \u00d7 3<\/span>
\nHere 2 and 3 have formed the groups of three.
\nThus, 46656 is a perfect cube.
\n<\/p>\n
\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) Prime factorisation of 243, is:
\n243 = 3 \u00d7 3 \u00d7 3<\/span> \u00d7 3 \u00d7 3 = 33<\/sup> \u00d7 3 \u00d7 3
\nHere, number 3 is required to make 3 \u00d7 3 a group of three, i.e., 3 \u00d7 3 \u00d7 3
\nThus, the required smallest number to be multiplied is 3.
\n
\n(ii) Prime factorisation of 256, is:
\n256 = 2 \u00d7 2 \u00d7 2<\/span> \u00d7 2 \u00d7 2 \u00d7 2<\/span> \u00d7 2 \u00d7 2 = 23<\/sup> \u00d7 23<\/sup> \u00d7 2 \u00d7 2
\nHere, a number 2 is needed to make 2 \u00d7 2 a group of three, i.e., 2 \u00d7 2 \u00d7 2
\nThus, the required smallest number to be multiplied is 2.
\n
\n(iii) Prime factorisation of 72, is:
\n72 = 2 \u00d7 2 \u00d7 2<\/span> \u00d7 3 \u00d7 3 = 23<\/sup> \u00d7 3 \u00d7 3
\nHere, a number 3 is required to make 3 \u00d7 3 a group of three, i.e. 3 \u00d7 3 \u00d7 3
\nThus, the required smallest number to be multiplied is 3.
\n
\n(iv) Prime factorisation of 675, is:
\n675 = 3 \u00d7 3 \u00d7 3<\/span> \u00d7 5 \u00d7 5 = 33<\/sup> \u00d7 5 \u00d7 5
\nHere, a number 5 is required to make 5 \u00d7 5 a group of three to make it a perfect cube, i.e. 5 \u00d7 5 \u00d7 5
\nThus, the required smallest number is 5.
\n
\n(v) Prime factorisation of 100, is:
\n100 = 2 \u00d7 2 \u00d7 5 \u00d7 5
\nHere, number 2 and 5 are needed to multiplied 2 \u00d7 2 \u00d7 5 \u00d7 5 to make it a perfect cube, i.e., 2 \u00d7 2 \u00d7 2 \u00d7 5 \u00d7 5 \u00d7 5
\nThus, the required smallest number to be multiplied is 2 \u00d7 5 = 10.
\n<\/p>\n
\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) 92
\n(v) 704
\nSolution:
\n(i) Prime factorisation of 81, is:
\n81 = 3 \u00d7 3 \u00d7 3<\/span> \u00d7 3 = 33<\/sup> \u00d7 3
\nHere, a number 3 is the number by which 81 is divided to make it a perfect cube,
\ni.e., 81 \u00f7 3 = 27 which is a perfect cube.
\nThus, the required smallest number to be divided is 3.
\n
\n(ii) Prime factorisation of 128, is:
\n128 = 2 \u00d7 2 \u00d7 2<\/span> \u00d7 2 \u00d7 2 \u00d7 2<\/span> \u00d7 2 = 23<\/sup> \u00d7 23<\/sup> \u00d7 2
\nHere, a number 2 is the smallest number by which 128 is divided to make it a perfect cube,
\ni.e., 128 \u00f7 2 = 64 which is a perfect cube.
\nThus, 2 is the required smallest number.
\n
\n(iii) Prime factorisation of 135 is:
\n135 = 3 \u00d7 3 \u00d7 3<\/span> \u00d7 5 = 33<\/sup> \u00d7 5
\nHere, 5 is the smallest number by which 135 is divided to make a perfect cube,
\ni.e., 135 \u00f7 5 = 27 which is a perfect cube.
\nThus, 5 is the required smallest number.
\n
\n(iv) Prime factorisation of 192 is:
\n192 = 2 \u00d7 2 \u00d7 2<\/span> \u00d7 2 \u00d7 2 \u00d7 2<\/span> \u00d7 3 = 23<\/sup> \u00d7 23<\/sup> \u00d7 3
\nHere, 3 is the smallest number by which 192 is divided to make it a perfect cube,
\ni.e., 192 \u00f7 3 = 64 which is a perfect cube.
\nThus, 3 is the required smallest number.
\n
\n(v) Prime factorisation of 704 is:
\n704 = 2 \u00d7 2 \u00d7 2<\/span> \u00d7 2 \u00d7 2 \u00d7 2<\/span> \u00d7 11 = 23<\/sup> \u00d7 23<\/sup> \u00d7 11
\nHere, 11 is the smallest number by which 704 is divided to make it a perfect cube,
\ni.e., 704 \u00f7 11 = 64 which is a perfect cube.
\nThus, 11 is the required smallest number.
\n<\/p>\n
\nParikshit makes a cuboid of plasticine of sides 5 cm, 2 cm, 5 cm. How many such cuboids will be needed to form a cube?
\nSolution:
\nThe sides of the cuboid are given as 5 cm, 2 cm and 5 cm.
\nVolume of the cuboid = 5 cm \u00d7 2 cm \u00d7 5 cm = 50 cm3<\/sup>
\nFor the prime factorisation of 50, we have
\n50 = 2 \u00d7 5 \u00d7 5
\nTo make it a perfect cube, we must have
\n2 \u00d7 2 \u00d7 2 \u00d7 5 \u00d7 5 \u00d7 5
\n= 20 \u00d7 (2 \u00d7 5 \u00d7 5)
\n= 20 \u00d7 volume of the given cuboid
\nThus, the required number of cuboids = 20.<\/p>\nMore CBSE Class 8 Study Material<\/h4>\n
\n