Question

Which of the following numbers are not perfect cubes?
(i) 216
(ii) 128
(iii) 1000
(iv) 100
(v) 46656

Answer 1

(i) 216 is the cube of 6

(iii) 1000 is the cube of 10

(v) 46656 is the cube of 36

therefore 100 and 128 are not perfect cubes

Answer 2

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(i) Prime factorisation of 216 is:

216 = 2 × 2 × 2 × 3 × 3 × 3

In the above factorisation, 2 and 3 have formed a group of three.

Thus, 216 is a perfect cube

ii) Prime factorisation of 128 is:

128 = 2 × 2 × 2 × 2 × 2 × 2 × 2

Here, 2 is left without making a group of three.

Thus 128 is not a perfect cube.

iii) Prime factorisation of 1000, is:

1000 = 2 × 2 × 2 × 5 × 5 × 5

Here, no number is left for making a group of three.

Thus, 1000 is a perfect cube.

iv) Prime factorisation of 100, is:

100 = 2 × 2 × 5 × 5

Here 2 and 5 have not formed a group of three.

Thus, 100 is not a perfect cube.

v) Prime factorisation of 46656 is:

46656 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 3 × 3 × 3

Here 2 and 3 have formed the groups of three.

Thus, 46656 is a perfect cube.

Hope it's help You❤️