Answer
$$\dfrac{3\sqrt3}{2}$$
Work Step by Step
Simplify the given expression to obtain:
\begin{align*}
&=\sqrt{\dfrac{(-3)(-3)(-3)(-3)}{12}}\\\\
&=\sqrt{\dfrac{81}{12}}\\\\
\end{align*}
RECALL:
(1) For any real numbers $a \ge 0, b\ge0$, $\sqrt{ab}=\sqrt{a} \cdot \sqrt{b}$
(2) For any real numbers $a \ge 0, b\gt 0$, $\sqrt{\dfrac{a}{b}}=\dfrac{\sqrt{a}}{\sqrt{b}}$
Use rule (2) above to obtain:
\begin{align*}
\sqrt{\dfrac{81}{12}}&=\dfrac{\sqrt{81}}{\sqrt{12}}\\\\
&=\dfrac{9}{\sqrt{12}}
\end{align*}
Rationalize the denominator by multiplying $\sqrt3$ to both the numerator and denominator to obtain:
\begin{align*}
&=\dfrac{9}{\sqrt{12}} \cdot \dfrac{\sqrt3}{\sqrt3}\\\\
&=\dfrac{9\sqrt3}{\sqrt{36}}\\\\
&=\dfrac{9\sqrt3}{6}
\end{align*}
Simplify by cancelling out the common factor $3$ to obtain:
\begin{align*}
\require{cancel}
&=\dfrac{\cancel{9}^3\sqrt3}{\cancel{6}^2}\\\\
&=\dfrac{3\sqrt3}{2}
\end{align*}
