If integer k > 100, what's the smallest possible integer value of the cubic root of k^2?

Question

Please explain

Answer 1

The prime factorization of K^2 must consist of multiples of three identical prime factors.
For example:
(125)(125) = (5x5x5)(5x5x5) has six factors of five and will have an integer cube root, namely 25 [<==answer]
The next smaller integer, 4:
(4x4x4)(4x4x4) has an integer cube root, but 4x4x4 = 64 is less that 100.