Answer
$-\sqrt{42}$
Work Step by Step
Using $i=\sqrt{-1},$ $i^2=-1,$ and the properties of radicals, the given expression, $
\sqrt{-6}\sqrt{-7}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{-1}\sqrt{6}\cdot\sqrt{-1}\sqrt{7}
\\\\=
i\sqrt{6}\cdot i\sqrt{7}
\\\\=
i(i)\sqrt{6(7)}
\\\\=
i^2\sqrt{42}
\\\\=
(-1)\sqrt{42}
\\\\=
-\sqrt{42}
.\end{array}
