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**1. For n ≥2, n^(1/n) is irrational.**

Hint provided: Use the fact that 2^n > n

**2. This is probably familiar to many.**

By contradiction, n = a^n/b^n

--> a^n = n(b^n)

--> n|a^n

--> n|a

Am I trying to force the same contradiction as with

*2^1/2 is rational*, that is, that a/b are not in lowest terms? Or do I need prime factorization to do something? Guidance is appreciated.

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