Answer
$\dfrac{\sqrt{14}}{2}$
Work Step by Step
Rationalizing the denominator of the given expression, $
\sqrt{\dfrac{7}{2}}
,$ we find:
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{7}{2}\cdot\dfrac{2}{2}}
\\\\=
\sqrt{\dfrac{14}{(2)^2}}
\\\\=
\dfrac{\sqrt{14}}{\sqrt{(2)^2}}
\\\\=
\dfrac{\sqrt{14}}{2}
.\end{array}