Answer
$-5\sqrt{6}$
Work Step by Step
Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $
\sqrt{-15}\sqrt{-10}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{-1}\sqrt{15}\cdot\sqrt{-1}\sqrt{10}
\\\\=
i\sqrt{15}\cdot i\sqrt{10}
\\\\=
i(i)\sqrt{15(10)}
\\\\=
i^2\sqrt{(3\cdot5)(2\cdot5)}
\\\\=
i^2\sqrt{(5)^2\cdot6}
\\\\=
5i^2\sqrt{6}
\\\\=
5(-1)\sqrt{6}
\\\\=
-5\sqrt{6}
.\end{array}
