Answer
$\frac{\sqrt{10xy}}{5y}$.
Work Step by Step
The given expression is
$=\sqrt{\frac{2x}{5y}}$
Use quotient rule.
$=\frac{\sqrt{2x}}{\sqrt{5y}}$
Multiply the numerator and the denominator by $\sqrt{5y}$.
$=\frac{\sqrt{2x}}{\sqrt{5y}}\cdot \frac{\sqrt{5y}}{\sqrt{5y}}$
Use product rule.
$=\frac{\sqrt{2x\cdot 5y}}{5y}$
Simplify.
$=\frac{\sqrt{10xy}}{5y}$.
