## Elementary Algebra

$\dfrac{\sqrt{10xy}}{5y}$
Using the properties of radicals, the given expression, $\dfrac{\sqrt{2x}}{\sqrt{5y}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt{2x}}{\sqrt{5y}}\cdot\dfrac{\sqrt{5y}}{\sqrt{5y}} \\\\= \dfrac{\sqrt{2x(5y)}}{(\sqrt{5y})^2} \\\\= \dfrac{\sqrt{10xy}}{5y} .\end{array} Note that all variables are assumed to have positive values.