# Math Help - abstract algebra proof

1. ## abstract algebra proof

a)let a be a positive integer.If square root of a is rational, prove that square root of a is an integer.

b)let r be a rational number and a an integer such that r^n = a .Prove that r is an integer.

Let $r=\frac{p}{q}$, reduced. Then $q^n\big|p^n$ and so $q\big|p$. So $r\in\mathbb{Z}$.