Answer
$5i\sqrt{3}$
Work Step by Step
Using $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b},$ the given expression, $
\sqrt{-75}
,$ is equivalent to
\begin{align*}
&
\sqrt{-1}\cdot\sqrt{25}\cdot\sqrt{3}
\\&=
\sqrt{-1}\cdot5\cdot\sqrt{3}
.\end{align*}
Since $i=\sqrt{-1},$ the expression above is equivalent to
\begin{align*}\require{cancel}
&
i\cdot5\cdot\sqrt{3}
\\&=
5i\sqrt{3}
.\end{align*}
