Answer
$\dfrac{3\sqrt[]{y}}{y}$
Work Step by Step
Multiplying both the numerator and the denominator by a factor that will make the denominator a perfect power of the radical, the rationalized-denominator form of the given expression, $
\sqrt[]{\dfrac{9}{y}}
,$ is
\begin{array}{l}\require{cancel}
\sqrt[]{\dfrac{9}{y}\cdot\dfrac{y}{y}}
\\\\=
\sqrt[]{\dfrac{9}{y^2}\cdot y}
\\\\=
\sqrt[]{\left( \dfrac{3}{y} \right)^2\cdot y}
\\\\=
\dfrac{3}{y}\sqrt[]{y}
\\\\=
\dfrac{3\sqrt[]{y}}{y}
.\end{array}
