Question

find the smallest number by which the number 5184 should be multiplied so that the product is a perfect cube and also find the cube root

Answer 1

Find the prime factors:

5184  = 2⁶ x 3⁴

Find k:

5184  = 2⁶ x 3⁴

For it to be a perfect cube, the exponents must be in the multiple of 3s

5184k  = 2⁶ x 3⁶

Therefore k = 3² = 9

Find the number:

The number = 5184 x 9 = 46656

Find the cube root:

46656  = 2⁶ x 3⁶

Divide the exponent by 3 to get the cube root:

∛46656 = 2² x 3² = 4 x 9 = 36

Answer: The smallest number to be multiplied is 9 and the cube root of the perfect cube is 36.