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