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

$\dfrac{\sqrt[]{7x}}{5y^{2}}$
Simplifying the given expression, $\sqrt[]{\dfrac{21x^2y}{75xy^5}} ,$ results to \begin{array}{l}\require{cancel} \sqrt[]{\dfrac{\cancel{3}\cdot7x^{2-1}y^{1-5}}{\cancel{3}\cdot25}} \\\\= \sqrt[]{\dfrac{7x^{1}y^{-4}}{25}} \\\\= \sqrt[]{\dfrac{7x}{25y^{4}}} \\\\= \dfrac{\sqrt[]{7x}}{\sqrt[]{25y^{4}}} \\\\= \dfrac{\sqrt[]{7x}}{\sqrt[]{(5y^{2})^2}} \\\\= \dfrac{\sqrt[]{7x}}{5y^{2}} .\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.