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) 81(ii) 128 (iii) 135
Answer» (i) 81 = 3 × 3 × 3 × 3 Here, one 3 is left which is not in a triplet. If we divide 81 by 3, then it will become a perfect cube. Thus, 81 ÷ 3 = 27 = 3 × 3 × 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 × 2 × 2 × 2 × 2 × 2 × 2 Here, one 2 is left which is not in a triplet. If we divide 128 by 2, then it will become a perfect cube. Thus, 128 ÷ 2 = 64 = 2 × 2 × 2 × 2 × 2 × 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 × 3 × 3 × 5 Here, one 5 is left which is not in a triplet. If we divide 135 by 5, then it will become a perfect cube. Thus, 135 ÷ 5 = 27 = 3 × 3 × 3 is a perfect cube. Hence, the smallest number by which 135 should be divided to make it a perfect cube is 5.

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

Answer»

(i) 81 = 3 × 3 × 3 × 3

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

If we divide 81 by 3, then it will become a perfect cube.

Thus, 81 ÷ 3 = 27 = 3 × 3 × 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 × 2 × 2 × 2 × 2 × 2 × 2 Here, one 2 is left which is not in a triplet.

If we divide 128 by 2, then it will become a perfect cube. Thus, 128 ÷ 2 = 64 = 2 × 2 × 2 × 2 × 2 × 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 × 3 × 3 × 5

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

If we divide 135 by 5, then it will become a perfect cube.

Thus, 135 ÷ 5 = 27 = 3 × 3 × 3 is a perfect cube.

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