Answer
$5x\sqrt[]{2x}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To simplify the given expression, $
\sqrt[]{50x^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[]{25x^2\cdot2x}
\\\\=
\sqrt[]{(5x)^2\cdot2x}
\\\\=
5x\sqrt[]{2x}
.\end{array}