Answer
$9|a|$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the properties of radicals to simplify the given expression, $
\sqrt{81a^2}
.$
$\bf{\text{Solution Details:}}$
Using $\sqrt[n]{x^n}=|x|$ if $n$ is even and $\sqrt[n]{x^n}=x$ if $n$ is odd, then
\begin{array}{l}\require{cancel}
\sqrt{81a^2}
\\\\=
\sqrt{(9a)^2}
\\\\=
|9a|
\\\\=
|9|\cdot|a|
\\\\=
9|a|
.\end{array}
