Intermediate Algebra (6th Edition)

$\dfrac{x\sqrt[]{2x}}{7y^2}$
Using the properties of radicals, the given expression, $\sqrt[]{\dfrac{2x^3}{49y^4}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt[]{\dfrac{x^2}{49y^4}\cdot2x} \\\\= \sqrt[]{\left( \dfrac{x}{7y^2} \right)^2\cdot2x} \\\\= \dfrac{x}{7y^2}\sqrt[]{2x} \\\\= \dfrac{x\sqrt[]{2x}}{7y^2} .\end{array} Note that all variables are assumed to have positive real numbers.