Answer
$-3+i\sqrt{2}$
Work Step by Step
Using $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}$ the given expression, $
\sqrt{-2}-3
,$ is equivalent to
\begin{align*}
&
\sqrt{-1}\cdot\sqrt{2}-3
\\&=
i\sqrt{2}-3
&\text{ (use $i=\sqrt{-1}$)}
\\&=
-3+i\sqrt{2}
.\end{align*}
Hence, the given expression simplifies to $
-3+i\sqrt{2}
$.
