#### Answer

$\frac{\sqrt 6}{12}$

#### Work Step by Step

Recall that we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $\sqrt \frac{1}{24}$, simplifies to:
$\sqrt {\frac{1}{24}\times\frac{6}{6}}$
=$\sqrt {\frac{1\times6}{24\times6}}$
=$\sqrt {\frac{6}{144}}$
=$\frac{\sqrt 6}{\sqrt {144}}$
=$\frac{\sqrt 6}{12}$