Answer
$\dfrac{\sqrt{21}}{3}$
Work Step by Step
Multiplying both the numerator and the denominator by $
\sqrt{3}
$, then the rationalized-denominator form of the given expression, $
\sqrt{\dfrac{7}{3}}
,$ is equivalent to
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{7}{3}\cdot\dfrac{3}{3}}
\\\\=
\sqrt{\dfrac{21}{(3)^2}}
\\\\=
\dfrac{\sqrt{21}}{\sqrt{(3)^2}}
\\\\=
\dfrac{\sqrt{21}}{3}
.\end{array}