Find the smallest number by which 500 should be multiplied to get a perfect cube and also find cube root - Maths - Cubes and Cube Roots

Question

Find the smallest number by which 500 should be multiplied to
get a perfect cube and also find cube root of perfect cube
obtained

Varun.Rawat · Accepted Answer

The prime factorisation of 500 is 500 =
2×2×5×5×5Since the prime factor 2 does not
occur in the group of 3, hence500 is not a perfect cube In order to
make it a perfect cube, we have to multiply it by 2 Hence, smallest
number by which 500 is to be multiplied in order to make it a
perfect cube = 2Now, 500 × 2 = 1000 perfect cube numberNow,
10003 = 2×2×2×5×5×53 = 2 × 5 =
10

Find the smallest number by which 500 should be multiplied to get a perfect cube and also find cube root of perfect cube obtained.