Answer
$\dfrac{\sqrt{3}}{4}$
Work Step by Step
Recall, we are not allowed to have radicals in the denominator of a fraction. Using the properties of radicals, the given expression, $
\dfrac{\sqrt{9}}{\sqrt{48}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{9}{48}}
\\\\=
\sqrt{\dfrac{\cancel{3}\cdot3}{\cancel{3}\cdot16}}
\\\\=
\sqrt{\dfrac{3}{16}}
\\\\=
\dfrac{\sqrt{3}}{\sqrt{16}}
\\\\=
\dfrac{\sqrt{3}}{\sqrt{(4)^2}}
\\\\=
\dfrac{\sqrt{3}}{4}
.\end{array}