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