Square root property proof Can anyone provide a link to a proof of the following square root property $\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}$. Could not find it online anywhere.

By the definition of square-root, $x=\sqrt{y}\hspace{.15cm}$ means that $x^2=y$.  
Assuming that $a,b\in\mathbb{R}$ with $a\geq 0$ and $b>0$, then we can simply compute:
\begin{align*}
\left(\frac{\sqrt{a}}{\sqrt{b}}\right)^2&=\frac{\sqrt{a}}{\sqrt{b}}\cdot \frac{\sqrt{a}}{\sqrt{b}}
=\frac{\sqrt{a}\cdot \sqrt{a}}{\sqrt{b}\cdot\sqrt{b}}=\frac{a}{b}
\end{align*} 
Therefore, $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}\hspace{.25cm}$
Note that I used the fact that $\frac{a}{b}\cdot \frac{c}{d}=\frac{ac}{bd}$
