Question

Divide 259875 by the smallest number so that the quotient is a perfect cube alsso find the cube root of the quotient​

Answer 1

Since 3 × 5 × 7 × 11 are unpaired 259875 should be divided by 3 × 5 × 7 × 11 we get

Pairs for cube root = 3 × 5.

Since 7 is unpaired so 259875 should be divided by 7 to get a perfect cube 259875 ÷ 7 = 37125

The cube root of 37125 is 33.359

Answer 2

Answer:

Prime factorising, 259875=(3×3×3)×(5×5×5)×7×11.

We know, a perfect cube has multiples of 3 as powers of prime factors.

Here, the prime factor 7 and 11 does not appear in triplet form.

Therefore, 259875 is not a perfect cube.

Since in the factorization, 7 and 11 appears only one time, we must divide the number 259875 by 7×11=77, then the quotient is a perfect cube.

∴259875÷77=3375

=15×15×15=15

3

, which is a perfect cube.

∴ The smallest number by which 259875 should be divided to make it a perfect cube is 77.