Answer
$10i\sqrt{3}$
Work Step by Step
Using the properties of radicals and that $i=\sqrt{-1}$, then the given expression, $
\sqrt{-300}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{-1}\cdot\sqrt{300}
\\\\=
i\cdot\sqrt{100\cdot3}
\\\\=
i\cdot\sqrt{(10)^2\cdot3}
\\\\=
i\cdot10\sqrt{3}
\\\\=
10i\sqrt{3}
.\end{array}