#### Answer

$\dfrac{\sqrt[]{14a}}{6}$

#### Work Step by Step

Rationalizing the denominator of the given expression, $
\sqrt[]{\dfrac{7a}{18}}
,$ we find:
\begin{array}{l}\require{cancel}
\sqrt[]{\dfrac{7a}{18}\cdot\dfrac{2}{2}}
\\\\=
\sqrt[]{\dfrac{14a}{36}}
\\\\=
\dfrac{\sqrt[]{14a}}{\sqrt[]{36}}
\\\\=
\dfrac{\sqrt[]{14a}}{\sqrt[]{(6)^2}}
\\\\=
\dfrac{\sqrt[]{14a}}{6}
.\end{array}
* Note that it is assumed that all variables represent positive numbers.