1.4. Natural Numbers, Integers, and Rational Numbers
Example 1.4.6: n-th Root is not Rational
Proofs that show that something is not the case call out for proofs by contradiction. Thus, you might want to start out a possible proof as follows:
Assume p1/n is rational, i.e. p1/n = a/b
If this would result in a contradiction (perhaps to the fact that p is assumed to be a prime number), we would have a classical proof by contradiction.
Soooo ... any thoughts?