Q4 of 239 Page 45

Find the smallest number by which each of the following number must be divided to obtain a perfect cube.
625

625

Prime Factorization:

⇒ 625 = 5 × 5 × 5 × 5

= 5³ × 5

There is only one 5.

∴ 625 is not a perfect cube.

Since in factorization, 5 appear only one time, we should divide the number 625 by 5.

⇒ 625 ÷ 5 = 125

= 5 × 5 × 5

= 5³

∴ The smallest number by which the number 625 must be divided to obtain a perfect cube is 5.

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

192

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

704

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

243

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

256

Questions · 239

1. Real Number System

1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 5 5 6 6 1 1 1 1 2 2 2 2 3 3 3 3 1 1 1 1 1 2 2 2 2 2 2 2 2 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 6 6 1 2 2 2 2 2 3 3 3 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 7 7 1 1 1 1 2 2 2 2 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 5 5 5 5 5 5 5 5 6 6 6 6 6 7 7 7 7 7 8 8 8 8 8 9 10 10 10 10 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 5 5 5 5 5 6 6 6 6 6 6 6 6 7 1 1 1 1 1 1 2 2 2 2 2 2 3 3 3 3 3 3 4 4 4 4 4 4 1 1 1 1 1 1 1 2 3

Find the smallest number by which each of the following number must be divided to obtain a perfect cube.625