Answer
$-\sqrt{30}$
Work Step by Step
Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $
\sqrt{-3}\sqrt{-10}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{-1}\sqrt{3}\cdot\sqrt{-1}\sqrt{10}
\\\\=
i\sqrt{3}\cdot i\sqrt{10}
\\\\=
i(i)\sqrt{3(10)}
\\\\=
i^2\sqrt{30}
\\\\=
(-1)\sqrt{30}
\\\\=
-\sqrt{30}
.\end{array}