Answer
$9i$
Work Step by Step
Using $\sqrt{ab}=\sqrt{a}\cdot\sqrt{b},$ the given expression, $
\sqrt{-81}
,$ is equivalent to
\begin{align*}
&
\sqrt{-1}\cdot\sqrt{81}
\\&=
\sqrt{-1}\cdot9
.\end{align*}
Since $i=\sqrt{-1},$ the expression above is equivalent to
\begin{align*}\require{cancel}
&
i\cdot9
\\&=
9i
.\end{align*}
Hence, the simplified form of the given expression is $
9i
$.
