## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\dfrac{2}{3}$
$\bf{\text{Solution Outline:}}$ Use the properties of radicals to simplify the given expression, $\dfrac{\sqrt{20y}}{\sqrt{45y}} .$ $\bf{\text{Solution Details:}}$ Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt{20y}}{\sqrt{45y}} \\\\= \sqrt{\dfrac{20y}{45y}} \\\\= \sqrt{\dfrac{4\cancel{5y}}{9\cancel{5y}}} \\\\= \sqrt{\dfrac{4}{9}} \\\\= \sqrt{\left(\dfrac{2}{3}\right)^2} \\\\= \dfrac{2}{3} .\end{array}