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.
PLease help me this one.
This is proved here:
Quadratic irrational - Wikipedia, the free encyclopedia
Let $\displaystyle r=\frac{p}{q}$, reduced. Then $\displaystyle q^n\big|p^n$ and so $\displaystyle q\big|p$. So $\displaystyle r\in\mathbb{Z}$.b)let r be a rational number and a an integer such that r^n = a .Prove that r is an integer.