Answer
$\frac{\sqrt {15}}{12}$
Work Step by Step
The given expression is
$=\frac{\sqrt{5}}{\sqrt {48}}$
Factor as square terms.
$=\frac{\sqrt{5}}{\sqrt {16\cdot 3}}$
Use product property of square roots.
$=\frac{\sqrt{5}}{\sqrt {16}\cdot \sqrt {3}}$
Use $16=4^2$.
$=\frac{\sqrt{5}}{\sqrt {4^2}\cdot \sqrt {3}}$
Simplify.
$=\frac{\sqrt{5}}{4 \sqrt {3}}$
Multiply by $\frac{\sqrt {3}}{\sqrt {3}}$.
$=\frac{\sqrt{5}}{4 \sqrt {3}}\cdot \frac{\sqrt {3}}{\sqrt {3}}$
Use product property of square roots.
$=\frac{\sqrt {5\cdot 3}}{4\sqrt {3\cdot 3}}$
Simplify.
$=\frac{\sqrt {15}}{4\sqrt {9}}$
Use $9=3^2$.
$=\frac{\sqrt {15}}{4\sqrt {3^2}}$
Simplify.
$=\frac{\sqrt {15}}{4\cdot 3}$
$=\frac{\sqrt {15}}{12}$
