Answer
$\frac{\sqrt {15}}{5}d$
Work Step by Step
The given expression is
$=\sqrt{\frac{3d^2}{5}}$
Use quotient property of square roots.
$=\frac{\sqrt{3d^2}}{\sqrt{5}}$
Use product property of square roots.
$=\frac{\sqrt{3}\cdot \sqrt{d^2}}{\sqrt{5}}$
Simplify.
$=\frac{\sqrt{3}d}{\sqrt{5}}$
Multiply by $\frac{\sqrt {5}}{\sqrt {5}}$.
$=\frac{\sqrt{3}d}{\sqrt{5}}\cdot \frac{\sqrt {5}}{\sqrt {5}}$
Use product property of square roots.
$=\frac{\sqrt {3\cdot 5}d}{\sqrt {5\cdot 5}}$
Simplify.
$=\frac{\sqrt {3\cdot 5}d}{\sqrt {5^2}}$
$=\frac{\sqrt {15}}{5}d$
