Answer
$\dfrac{2}{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
