Question

3) By which smallest natural number 135 should be divided so that the
quotient is a perfect cube?​

Answer 1

Answer:

The number should be divided by 5

Explanation:

Prime factorised form of 135 = 5 × 3 × 3 × 3

( In factorised form of a perfect cube, all the number in prime factorised form should come thrice. Here, three 3 are present and one extra five is also present, so we could remove the 5 to make it a perfect cube.)

⟹ 135 = 5 × 3 × 3 × 3

⟹ 135 ÷ 5 = 5 × 3 × 3 × 3 ÷ 5

⟹ 27 = 3 × 3 × 3

⟹ 27 = 3³

⟹ √27 = 3

We should divide 135 by 5 to get a perfect cube.