Answer
$\dfrac{3\sqrt{y}}{y}$
Work Step by Step
Multiplying both the numerator and the denominator of the radical by $y$, 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}
Note that the value of the variable is assumed to be positive.
