Answer
$\dfrac{\sqrt{13}}{2}$
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, $
\sqrt{3\dfrac{1}{4}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{13}{4}}
\\\\=
\dfrac{\sqrt{13}}{\sqrt{4}}
\\\\=
\dfrac{\sqrt{13}}{\sqrt{(2)^2}}
\\\\=
\dfrac{\sqrt{13}}{2}
.\end{array}