Answer
$\dfrac{6\sqrt{2}}{y^{10}}$
Work Step by Step
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $
\sqrt{\dfrac{72}{y^{20}}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{72}}{\sqrt{y^{20}}}
\\\\=
\dfrac{\sqrt{36\cdot2}}{\sqrt{(y^{10})^2}}
\\\\=
\dfrac{\sqrt{(6)^2\cdot2}}{\sqrt{(y^{10})^2}}
\\\\=
\dfrac{6\sqrt{2}}{y^{10}}
.\end{array}
Note that variables are assumed to have positive real numbers.
