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