## Elementary Algebra

$\dfrac{8}{3}\sqrt{5xy}$
Using the properties of radicals, the given expression, $\dfrac{4}{3}\sqrt{20xy} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{4}{3}\sqrt{4\cdot5xy} \\\\= \dfrac{4}{3}\sqrt{(2)^2\cdot5xy} \\\\= \dfrac{4}{3}\cdot2\sqrt{5xy} \\\\= \dfrac{8}{3}\sqrt{5xy} .\end{array} Note that all of the variables are assumed to represent non-negative real numbers.