(In reply to
An idea by Jer)
But we can easily get the product of two cube roots of positive nonperfect 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.

Posted by Charlie
on 20150814 13:28:01 