## Elementary Algebra

$\dfrac{x\sqrt{2x}}{3}$
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.