## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$9|a|$
$\bf{\text{Solution Outline:}}$ 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}