Answer
$\frac{\sqrt{6}}{3}y$.
Work Step by Step
The given expression is
$=\sqrt{\frac{2y^2}{3}}$
Use quotient property of square roots.
$=\frac{\sqrt{2y^2}}{\sqrt{3}}$
Multiply by $\frac{\sqrt{3}}{\sqrt{3}}$.
$=\frac{\sqrt{2y^2}}{\sqrt{3}}\cdot \frac{\sqrt{3}}{\sqrt{3}}$
Use product property of square roots.
$=\frac{\sqrt{2y^2\cdot 3}}{\sqrt{3\cdot 3}}$
$=\frac{\sqrt{6y^2}}{\sqrt{3^2}}$
Use product property of square roots.
$=\frac{\sqrt{6}\sqrt{y^2}}{\sqrt{3^2}}$
Simplify.
$=\frac{\sqrt{6}}{3}y$.
