calculus - Evaluate $limlimits_{n to infty}sumlimits_{k=0}^n dfrac{sqrt{n}}{n+k^2}(n=1,2,cdots)$

I tried to change it into a Riemann sum but failed, since

\begin{align*}
\lim_{n \to \infty}\sum_{k=0}^n \frac{\sqrt{n}}{n+k^2}=\lim_{n \to \infty}\frac{1}{n}\sum_{k=0}^n \frac{\sqrt{n}}{1+(k/\sqrt{n})^2}
,\end{align*}
which is not a standard form. Maybe, it need apply the squeeze theorem, but how to evaluate the bound.

By the way, WA gives its result
\begin{align*}
\lim_{n \to \infty}\sum_{k=0}^n \frac{\sqrt{n}}{n+k^2}=\frac{\pi}{2}.
\end{align*}