## NCERT Solutions for class 8 Maths Chapter 6: Cubes and Cube Roots## Exercise 6.1
216 = 2 × 108 216 = 2 × 2 × 54 216 = 2 × 2 × 2 × 27 216 = 2 × 2 × 2 × 3 × 9 216 = 2 × 2 × 2 × 3 × 3 × 3 Here, 2 and 3 forms the triplet. Hence, 216 is a perfect cube. Cube root of 216 = 2 × 3 Cube root of 216 = 6
128 = 2 × 64 128 = 2 × 2 × 32 128 = 2 × 2 × 2 × 16 128 = 2 × 2 × 2 × 2 × 8 128 = 2 × 2 × 2 × 2 × 2 × 4 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 Here, two triplets are formed. But, a 2 number is left and does not form any triplet. Hence, 128 is not a perfect cube.
1000 = 2 × 500 1000 = 2 × 2 × 250 1000 = 2 × 2 × 2 × 125 1000 = 2 × 2 × 2 × 5 × 25 1000 = 2 × 2 × 2 × 5 × 5 × 5 Here, 2 and 5 forms the triplet. Hence, 1000 is a perfect cube. Cube root of 1000 = 2 × 5 Cube root of 1000 = 10
100 = 2 × 50 100 = 2 × 2 × 25 100 = 2 × 2 × 5 × 5 Here, neither 2 nor 5 form a triplet. Hence, it is not a perfect cube.
46656 = 2 × 23328 46656 = 2 × 2 × 11664 46656 = 2 × 2 × 2 × 5832 46656 = 2 × 2 × 2 × 2 × 2916 46656 = 2 × 2 × 2 × 2 × 2 × 1458 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 729 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 243 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 81 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 27 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 9 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 Here, 2 and 3 forms the triplets. Hence, 46656 is a perfect square. Cube root of 46656 = 2 × 2 × 3 × 3 Cube root of 46656 = 36 Thus, among all options,
243 = 3 × 81 243 = 3 × 3 × 27 243 = 3 × 3 × 3 × 9 243 = 3 × 3 × 3 × 3 × 3 To form a cube, multiply the given number by 3. 243 × 3 = 3 × 3 × 3 × 3 × 3 × 3 729 = 3 × 3 × 3 × 3 × 3 × 3 Cube root of 729 = 3 × 3 Cube root of 729 = 9
256 = 2 × 128 256 = 2 × 2 × 64 256 = 2 × 2 × 2 × 32 256 = 2 × 2 × 2 × 2 × 16 256 = 2 × 2 × 2 × 2 × 2 × 8 256 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 To form a cube, multiply the given number by 2. 256 × 2 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 Cube root of 512 = 2 × 2 × 2 Cube root of 512 = 8
72 = 2 × 36 72 = 2 × 2 × 18 72 = 2 × 2 × 2 × 9 72 = 2 × 2 × 2 × 3 × 3 To form a cube, multiply the given number by 3. 72 × 3 = 2 × 2 × 2 × 3 × 3 × 3 216 = 2 × 2 × 2 × 3 × 3 × 3 Cube root of 216 = 2 × 3 Cube root of 216 = 6
675 = 5 × 135 675 = 5 × 5 × 27 675 = 5 × 5 × 3 × 9 675 = 5 × 5 × 3 × 3 × 3 To form a cube, multiply the given number by 5. 675 × 5 = 5 × 5 × 5 × 3 × 3 × 3 3375 = 5 × 5 × 5 × 3 × 3 × 3 Cube root of 3375 = 5 × 3 Cube root of 3375 = 15
100 = 2 × 50 100 = 2 × 2 × 25 100 = 2 × 2 × 5 × 5 To form a cube, multiply the given number by 2 and 5, i.e., 10. 100 × 2 × 5 = 2 × 2 × 5 × 5 × 2 × 5 1000 = 2 × 2 × 2 × 5 × 5 × 5 Cube root of 1000 = 2 × 5 Cube root of 1000 = 10
81 = 3 × 27 81 = 3 × 3 × 9 81 = 3 × 3 × 3 × 3 To form a cube, divide the given number by 3. 81/3 = (3 × 3 × 3 × 3)/3 27 = 3 × 3 × 3 Cube root of 27 = 3
128 = 2 × 64 128 = 2 × 2 × 32 128 = 2 × 2 × 2 × 16 128 = 2 × 2 × 2 × 2 × 8 128 = 2 × 2 × 2 × 2 × 2 × 4 128 = 2 × 2 × 2 × 2 × 2 × 2 × 2 To form a cube, divide the given number by 2. 128/2 = (2 × 2 × 2 × 2 × 2 × 2 × 2)/2 64 = 2 × 2 × 2 × 2 × 2 × 2 Cube root of 64 = 2 × 2 Cube root of 64 = 4
135 = 5 × 27 135 = 5 × 3 × 9 135 = 5 × 3 × 3 × 3 To form a cube, divide the given number by 5. 135/5 = (5 × 3 × 3 × 3)/ 5 27 = 3 × 3 × 3 Cube root of 27 = 3
192 = 3 × 64 192 = 3 × 2 × 32 192 = 3 × 2 × 2 × 16 192 = 3 × 2 × 2 × 2 × 8 192 = 3 × 2 × 2 × 2 × 2 × 4 192 = 3 × 2 × 2 × 2 × 2 × 2 × 2 To form a cube, divide the given number by 3. 192/3 = (3 × 2 × 2 × 2 × 2 × 2 × 2)/3 64 = 2 × 2 × 2 × 2 × 2 × 2 Cube root of 64 = 2 × 2 Cube root of 64 = 4
704 = 2 × 352 704 = 2 × 2 × 176 704 = 2 × 2 × 2 × 88 704 = 2 × 2 × 2 × 2 × 44 704 = 2 × 2 × 2 × 2 × 2 × 22 704 = 2 × 2 × 2 × 2 × 2 × 2 × 11 To form a cube, divide the given number by 11. 704/11 = (2 × 2 × 2 × 2 × 2 × 2 × 11)/11 64 = 2 × 2 × 2 × 2 × 2 × 2 Cube root of 64 = 2 × 2 Cube root of 64 = 4
To form a cube, the cuboids of sides 5 cm, 2 cm, and 2 cm are required, i.e., 2 × 2 × 5 = 20 cuboids = 5 × 2 × 5 × 2 × 2 × 5 = 5 × 5 × 5 × 2 × 2 × 2 ## Exercise 6.2
64 = 2 × 32 64 = 2 × 2 × 16 64 = 2 × 2 × 2 × 8 64 = 2 × 2 × 2 × 2 × 4 64 = 2 × 2 × 2 × 2 × 2 × 2 The factor in a cube forms a triplet. Here, two triplets of 2 are created. Cube root of 64 = 2 × 2 Cube root of 64 = 4
512 = 2 × 256 512 = 2 × 2 × 128 512 = 2 × 2 × 2 × 64 512 = 2 × 2 × 2 × 2 × 32 512 = 2 × 2 × 2 × 2 × 2 × 16 512 = 2 × 2 × 2 × 2 × 2 × 2 × 8 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 4 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 The factor in a cube forms a triplet. Here, three triplets of 2 are created. Cube root of 512 = 2 × 2 × 2 Cube root of 512 = 8
10648 = 2 × 5324 10648 = 2 × 2 × 2662 10648 = 2 × 2 × 2 × 1331 10648 = 2 × 2 × 2 × 11 × 121 10648 = 2 × 2 × 2 × 11 × 11 × 11 The factor in a cube forms a triplet. Here, two triplets of 2 and 11 are created. Cube root of 10648 = 2 × 11 Cube root of 10648 = 22
27000 = 3 × 9000 27000 = 3 × 3 × 3000 27000 = 3 × 3 × 3 × 1000 27000 = 3 × 3 × 3 × 2 × 500 27000 = 3 × 3 × 3 × 2 × 2 × 250 27000 = 3 × 3 × 3 × 2 × 2 × 2 ×125 27000 = 3 × 3 × 3 × 2 × 2 × 2 × 5 × 25 27000 = 3 × 3 × 3 × 2 × 2 × 2 × 5 × 5 × 5 The factor in a cube forms a triplet. Here, three triplets of 2, 3, and 5 are created. Cube root of 27000 = 3 × 2 × 5 Cube root of 27000 = 30
15625 = 5 × 3125 15625 = 5 × 5 × 625 15625 = 5 × 5 × 5 × 125 15625 = 5 × 5 × 5 × 5 × 25 15625 = 5 × 5 × 5 × 5 × 5 × 5 The factor in a cube forms a triplet. Here, two triplets of 5 are created. Cube root of 15625 = 5 × 5 Cube root of 15625 = 25
13824 = 2 × 6912 13824 = 2 × 2 × 3456 13824 = 2 × 2 × 2 × 1728 13824 = 2 × 2 × 2 × 2 × 864 13824 = 2 × 2 × 2 × 2 × 2 × 432 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 216 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 108 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 54 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 27 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 9 13824 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 The factor in a cube forms a triplet. Here, four triplets of 2 and 3 are created. Cube root of 13824 = 2 × 2 × 2 × 3 Cube root of 13824 = 24
110592 = 2 × 55296 110592 = 2 × 2 × 27648 110592 = 2 × 2 × 2 × 13824 110592 = 2 × 2 × 2 × 2 × 6912 110592 = 2 × 2 × 2 × 2 × 2 × 3456 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 1728 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 864 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 432 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 216 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 108 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 54 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 27 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 9 110592 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 The factor in a cube forms a triplet. Here, five triplets of 2 and 3 are created. Cube root of 110592 = 2 × 2 × 2 × 2 × 3 Cube root of 110592 = 48
46656 = 2 × 23328 46656 = 2 × 2 × 11664 46656 = 2 × 2 × 2 × 5832 46656 = 2 × 2 × 2 × 2 × 2916 46656 = 2 × 2 × 2 × 2 × 2 × 1458 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 729 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 243 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 81 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 27 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 9 46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3 The factor in a cube forms a triplet. Here, four triplets of 2 and 3 are created. Cube root of 46656 = 2 × 2 × 3 × 3 Cube root of 46656 = 36
175616 = 2 × 87808 175616 = 2 × 2 × 43904 175616 = 2 × 2 × 2 × 21952 175616 = 2 × 2 × 2 × 2 × 10976 175616 = 2 × 2 × 2 × 2 × 2 × 5488 175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2744 175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 1372 175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 686 175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 343 175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 49 175616 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 7 × 7 × 7 The factor in a cube forms a triplet. Here, four triplets of 2 and 7 are created. Cube root of 175616 = 2 × 2 × 2 × 7 Cube root of 175616 = 56
91125 = 5 × 18225 91125 = 5 × 5 × 3645 91125 = 5 × 5 × 5 × 729 91125 = 5 × 5 × 5 × 3 × 243 91125 = 5 × 5 × 5 × 3 × 3 × 81 91125 = 5 × 5 × 5 × 3 × 3 × 3 × 27 91125 = 5 × 5 × 5 × 3 × 3 × 3 × 3 × 9 91125 = 5 × 5 × 5 × 3 × 3 × 3 × 3 × 3 × 3 The factor in a cube forms a triplet. Here, three triplets of 5 and 3 are created. Cube root of 91125 = 5 × 3 × 3 Cube root of 91125 = 45
It is not always true. For example, Square of 35 = 1225 Cube of 35 = 42875 Here, the cube ends with 75. Hence, the above statement is not true.
For example, Cube of 1 = 1 Cube of 2 = 8 Next TopicNCERT Solutions for class 12 Maths |