Question

Find the smallest natural number by which 5184 should be multiplied so that the product is a perfect cube

Answer 1

Step-by-step explanation:

The prime factorization of 5184 is~

2×2×2×2×2×2×9×9

i.e.

$2 {}^{3} \times 2 {}^{3} \times 9 {}^{2}$

To be a perfect cube the factors must be 3 times

So, the smallest natural(positive) number that should be multiplied with 5184 to make it a perfect cube is 9

Verification:-

5184×9= 46656

which is a cube of 36