## Intermediate Algebra (12th Edition)

$10z\sqrt[]{3z}$
$\bf{\text{Solution Outline:}}$ To simplify the given expression, $\sqrt[]{300z^3} ,$ find a factor of the radicand that is a perfect power of the index. Then extract the root of that factor. Note that all variables are assumed to represent positive real numbers. $\bf{\text{Solution Details:}}$ Expressing the radicand of the expression above with a factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt[]{100z^2\cdot3z} \\\\= \sqrt[]{(10z)^2\cdot3z} \\\\= 10z\sqrt[]{3z} .\end{array}