Question

Find the smallest number by which 16875 be divided to get a perfect cube.Find the cube root of the number thus obtained.​

Answer 1

First we factor the number, To make it a perfect cube we divide the number by 5. Therefore, the smallest no by which 16875 must be divided to get a perfect cube is 5.

cube root of 5 is 1.70997594668

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Answer 2

Given: A number 16875

To find: (i) The smallest number by which it should be divided to get a   perfect cube

             (ii) The cube root of number obtained

Solution: The given number is 16875

Expressing the number as the product of it's prime factors:

16875 = (3 × 3 × 3) × (5 × 5 × 5) × 5

Prime factor 5 is appearing in the group of 4. Hence, 16875 should be divided by 5 to get a perfect cube.

16875 ÷ 5 = 3375

Finding cube root of 3375 using Prime Factorization Method:

3375 = (3 × 3 × 3) × (5 × 5 × 5)

∛3375 = 3 × 5 = 15

Hence, the smallest number by which 16875 must be divided to get a perfect cube is 5 and the cube root of the number obtained is 15.