But we can easily get the product of two cube roots of positive non-perfect cubes to be an integer: 12^(1/3) * 18^(1/3) = 6.
The 12 and the 18 of course come from 2*2*3 and 2*3*3 so the product is a perfect cube while the numbers are not. Substitute any two primes or relative primes.
re: An idea
