Answer
$3i$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt{-9}
,$ use the properties of radicals and the equivalence $i=\sqrt{-1}.$
$\bf{\text{Solution Details:}}$
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to\begin{array}{l}\require{cancel}
\sqrt{-1}\cdot\sqrt{9}
.\end{array}
Since $i=\sqrt{-1},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
i\sqrt{9}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
i\sqrt{(3)^2}
\\\\=
i(3)
\\\\=
3i
.\end{array}
