real analysis - How can I find $lim_{nrightarrowinfty}(1+frac{x}n)^{sqrt{n}}$?

How can I find $$\lim_{n\rightarrow\infty}\left(1+\frac{x}n\right)^{\sqrt{n}}\;?$$

I know $\lim_{n\rightarrow\infty}\left(1+\frac{x}n\right)^{n} = \exp (x)$ but I don't know how can I put the definition in this particular limit.

I know then, that $\lim_{n\rightarrow\infty}\big(1+\frac{x}n\big)=1$, but I don't think this is right to consider.

Answer

$$\lim_{n\rightarrow\infty}\left(1+\frac{x}n\right)^{\sqrt{n}} = \lim_{n\rightarrow\infty}\left[\left(1+\frac{x}n\right)^{{\frac{n}{x}}}\right]^{{\frac{x}{n}}{\sqrt{n}}}$$
From
$$\lim_{n\rightarrow\infty}\left[\left(1+\frac{x}n\right)^{{\frac{n}{x}}}\right]=e \quad \text{and} \quad \lim_{n\rightarrow\infty}{{\frac{x}{n}}{\sqrt{n}}}=0,$$ **, we get
$$\lim_{n\rightarrow\infty}\left(1+\frac{x}n\right)^{\sqrt{n}} = e^0=1$$

EDIT
I add the note bellow as my calculation was considered insufficiently justified

**and because the terms are positive, and we don't have an indeterminate case $0^0$ or $1^{\infty}$ or $\infty ^0,\;$