number theory - Prove that $2^{1/n}$ is irrational

Proof by contradiction, Assume $2^{1/n}$ is rational so:

$$2^{1/n} = \frac ab $$

where a,b have no common factors.

$$2 = \frac{a^n}{b^n}$$

$2$ divides LHS, therefore $2$ divides RHS
so $2$ divides $a^n$ or $2$ divides $b^n$ which implies $2$ divides $a$ or $2$ divides $b$.

Stuck on what to do next.