Answer
$\dfrac{6}{y\sqrt{2}}$
Work Step by Step
Multiplying both the numerator and the denominator by a factor that will make the numerator a perfect power of the radical, the rationalized-numerator form of the given expression, $
\dfrac{\sqrt[]{18}}{y}
,$ is
\begin{array}{l}\require{cancel}
\dfrac{\sqrt[]{18}}{y}\cdot\dfrac{\sqrt[]{2}}{\sqrt[]{2}}
\\\\=
\dfrac{\sqrt[]{36}}{y\sqrt{2}}
\\\\=
\dfrac{\sqrt[]{(6)^2}}{y\sqrt{2}}
\\\\=
\dfrac{6}{y\sqrt{2}}
.\end{array}
