1.4. Natural Numbers, Integers, and Rational Numbers

Example 1.4.6: n-th Root is not Rational

Prove that if p is a prime number, then p1/n, where n > 1, 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?

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