Find the smallest number by which each of the following numbers must b

1.	Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.(i) 192(ii) 704
Answer» (i) 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3 Here, one 3 is left which is not in a triplet. If we divide 192 by 3, then it will become a perfect cube. Thus, 192 ÷ 3 = 64 = 2 × 2 × 2 × 2 × 2 × 2 is a perfect cube. Hence, the smallest number by which 192 should be divided to make it a perfect cube is 3. (ii) 704 = 2 × 2 × 2 × 2 × 2 × 2 × 11 Here, one 11 is left which is not in a triplet. If we divide 704 by 11, then it will become a perfect cube. Thus, 704 ÷ 11 = 64 = 2 × 2 × 2 × 2 × 2 × 2 is a perfect cube. Hence, the smallest number by which 704 should be divided to make it a perfect cube is 11

Find the smallest number by which each of the following numbers must be divided to obtain a perfect cube.(i) 192(ii) 704

Answer»

(i) 192 = 2 × 2 × 2 × 2 × 2 × 2 × 3

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

If we divide 192 by 3, then it will become a perfect cube. Thus, 192 ÷ 3 = 64 = 2 × 2 × 2 × 2 × 2 × 2 is a perfect cube.

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

(ii) 704 = 2 × 2 × 2 × 2 × 2 × 2 × 11

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

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

Thus, 704 ÷ 11 = 64 = 2 × 2 × 2 × 2 × 2 × 2 is a perfect cube.

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