Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube

(i) 81 (ii) 128

(iii) 135 (iv) 192

(v) 704

(i) 81 = 3 x 3 x 3 x 3

Here, one 3 is left which is not forming a triplet.

So, if we divide 81 by 3, then it will become a perfect cube

Therefore,

= 27 = 3 x 3 x 3 is a perfect cube

Hence, the smallest number by which 81 should be divided to make it a perfect cube is 3

(ii) 128 = 2 x 2 x 2 x 2 x 2 x 2 x 2

Here, one 2 is left which is not forming a triplet.

Si, if we divide 128 by 2, then it will become a perfect cube

Therefore,

= 64 = 2 x 2 x 2 x 2 x 2 x 2 is a perfect cube

Hence, the smallest number by which 128 should be divided to make it a perfect cube is 2

(iii) 135 = 3 x 3 x 3 x 5

Here, one 5 is left which is not forming a triplet.

So, if we divide 135 by 5, then it will become a perfect cube

Therefore,

= 27 = 3 x 3 x 3 is a perfect cube

Hence, the smallest number by which 135 should be divided to make it a perfect cube is 5

(iv) 192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

Here, one 3 is left which is not forming a triplet.

So, if we divide 192 by 3, then it will become a perfect cube

Therefore,

= 64 = 2 x 2 x 2 x 2 x 2 x 2 is a perfect cube

Hence, the smallest number by which 192 should be divided to make it a perfect cube is 3

(v) 704 = 2 x 2 x 2 x 2 x 2 x 2 x 11

Here, one 11 is left which is not forming a triplet.

So, if we divide 704 by 11, then it will become a perfect cube.

Therefore,

= 64 = 2 x 2 x 2 x 2 x 2 x 2 is a perfect cube

Hence, the smallest number by which 704 should be divided to make it a perfect cube is 11

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