Answer
$\frac{x\sqrt y}{10}$
Work Step by Step
The quotient rule holds that $\sqrt[n] (\frac{a}{b})=\frac{\sqrt[n] a}{\sqrt[n] b}$ (where $\sqrt[n] a$ and $\sqrt[n] b$ are real numbers and $\sqrt[n] b$ is nonzero).
Therefore, $\sqrt (\frac{x^{2}y}{100})=\frac{\sqrt (x^{2}y)}{\sqrt 100}=\frac{\sqrt (x^{2})\times\sqrt y}{\sqrt 100}=\frac{x\sqrt y}{10}$
We know that $\sqrt (x^{2})=x$, because $(x)^{2}=x^{2}$. Also, we know that $\sqrt 100=10$, because $10^{2}=100$.