Answer
$\frac{3 \sqrt{35y}}{7y}$
Work Step by Step
The given expression is
$=\sqrt{\frac{45}{7y}}$
Use quotient property of square roots.
$=\frac{\sqrt{45}}{\sqrt{7y}}$
Factor as square terms.
$=\frac{\sqrt{9\cdot 5}}{\sqrt{7y}}$
Use product property of square roots.
$=\frac{\sqrt{9}\cdot \sqrt{5}}{\sqrt{7y}}$
Simplify.
$=\frac{3 \sqrt{5}}{\sqrt{7y}}$
Multiply by $\frac{\sqrt{7y}}{\sqrt{7y}}$.
$=\frac{3 \sqrt{5}}{\sqrt{7y}}\cdot \frac{\sqrt{7y}}{\sqrt{7y}}$
Use product property of square roots.
$=\frac{3 \sqrt{5\cdot 7y}}{\sqrt{(7y)^2}}$
Simplify.
$=\frac{3 \sqrt{35y}}{7y}$
