#### Answer

$10z\sqrt[]{3z}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
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}