## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

$\dfrac{\sqrt[]{5b}}{6a}$
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.