Establish the following facts:(a) is irrational for any prime p.(b) If a > 0 and is r...

Establish the following facts:

(a) is irrational for any prime p.

(b) If a > 0 and is rational, then must be an integer.

(c) For n ≥ 2, is irrational.

[Hint: Use the fact that 2n > n.]