Answer
$\dfrac{\sqrt[]{5b}}{6a}$
Work Step by Step
Simplifying the given expression, $
\sqrt[]{\dfrac{10ab^2}{72a^3b}}
,$ we find:
\begin{array}{l}\require{cancel}
\sqrt[]{\dfrac{\cancel{2}\cdot5a^{1-3}b^{2-1}}{\cancel{2}\cdot36}}
\\\\=
\sqrt[]{\dfrac{5a^{-2}b^{1}}{36}}
\\\\=
\sqrt[]{\dfrac{5b}{36a^{2}}}
\\\\=
\dfrac{\sqrt[]{5b}}{\sqrt[]{36a^{2}}}
\\\\=
\dfrac{\sqrt[]{5b}}{\sqrt[]{(6a)^{2}}}
\\\\=
\dfrac{\sqrt[]{5b}}{6a}
.\end{array}
The simplified form of the given expression already has a rationalized denominator.
* Note that it is assumed that all variables represent positive numbers.