Answer
$2i$
Work Step by Step
Using $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b},$ the given expression, $
\sqrt{-4}
,$ is equivalent to
\begin{align*}
&
\sqrt{-1}\cdot\sqrt{4}
\\&=
\sqrt{-1}\cdot2
.\end{align*}
Since $i=\sqrt{-1},$ the expression above is equivalent to
\begin{align*}\require{cancel}
&
i\cdot2
\\&=
2i
.\end{align*}