find the smallest no by which 675 should be multiplied so that the product is a perfect cube - Maths -

Question

find the smallest no by which 675 should be multiplied so that
the product is a perfect cube

Manbar Singh · Accepted Answer

The prime factorisation of 675 is given by,675 = 3×3×3×5×5Since the prime factor 5 does not occur in the group of 3, so 675 is not a perfect cube
In order to make 675 a perfect cube, it must be mutiplied by 5
Now,675 × 5 = 3375 perfect cube33753 = 3×3×3×5×5×53 = 3 × 5 = 15