Answer
$\dfrac{x\sqrt{2x}}{3}$
Work Step by Step
Using the properties of radicals, the given expression, $
\sqrt{\dfrac{2x^3}{9}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{x^2}{9}\cdot2x}
\\\\=
\sqrt{\left(\dfrac{x}{3}\right)^2\cdot2x}
\\\\=
\dfrac{x}{3}\sqrt{2x}
\\\\=
\dfrac{x\sqrt{2x}}{3}
.\end{array}
Note that all variables are assumed to have positive values.
