Answer
$\dfrac{3\sqrt{2xy}}{2y}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{\sqrt{72x}}{\sqrt{16y}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{72x}{16y}}
\\\\=
\sqrt{\dfrac{\cancel{8}(9)x}{\cancel{8}(2)y}}
\\\\=
\sqrt{\dfrac{9x}{2y}}
\\\\=
\sqrt{\dfrac{9x}{2y}\cdot\dfrac{2y}{2y}}
\\\\=
\sqrt{\dfrac{9x}{4y^2}\cdot2y}
\\\\=
\sqrt{\left(\dfrac{3}{2y}\right)^2\cdot2xy}
\\\\=
\dfrac{3}{2y}\sqrt{2xy}
\\\\=
\dfrac{3\sqrt{2xy}}{2y}
.\end{array}
Note that all variables are assumed to have positive values.
