I have to show that $\displaystyle \lim\sqrt[n]{n+\sqrt{n}}$ goes to 1 as $\displaystyle n\rightarrow\infty$.

I have that $\displaystyle \sqrt[n]{n}\leq \sqrt[n]{n+\sqrt{n}}\leq\sqrt[n]{2n}$

I know that $\displaystyle \sqrt[n]{n}\rightarrow 1$ via the binomial theorem.

If I can show that $\displaystyle \sqrt[n]{2n}\rightarrow 1$, I could use the Squeeze theorem.

Any ideas?