Answer
$2i\sqrt{6}$
Work Step by Step
Using $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ the given expression, $
\sqrt{-24}
,$ is equivalent to
\begin{align*}
&
\sqrt{-1}\cdot\sqrt{4}\cdot\sqrt{6}
\\&=
\sqrt{-1}\cdot2\cdot\sqrt{6}
\\&=
i\cdot2\cdot\sqrt{6}
\\&=
2i\sqrt{6}
&\text{ (use $i=\sqrt{-1}$)}
.\end{align*}
Hence, the given expression simplifies to $
2i\sqrt{6}
$.
