Proof that the limit of $a^{1/n}$ is one where $a>0$ is a real number and $n$ is a natural number

Question

Proof that the limit of $a^{1/n}$ is one where $a$ is a real number and $n$ is a natural number.

I am only allowed to use $N,\epsilon$-Proof and the Squeeze theorem. For some special cases like $a$ is a natural numeber I could show that this is true but I couldn't show the general case.