Answer
$\dfrac{\sqrt{14}}{2}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\sqrt{\dfrac{7}{2}}
,$ multiply both the numerator and the denominator by an expression that will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying the radicand by an expression equal to $1$ which will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{7}{2}\cdot\dfrac{2}{2}}
\\\\
\sqrt{\dfrac{14}{(2)^2}}
.\end{array}
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{14}}{\sqrt{(2)^2}}
\\\\=
\dfrac{\sqrt{14}}{2}
.\end{array}
