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

$\dfrac{6y\sqrt[]{y}}{x^2}$
Using the properties of radicals, the given expression, $\sqrt[]{\dfrac{36y^3}{x^4}} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{\sqrt[]{36y^3}}{\sqrt[]{x^4}} \\\\= \dfrac{\sqrt[]{36y^2\cdot y}}{\sqrt[]{x^4}} \\\\= \dfrac{\sqrt[]{(6y)^2\cdot y}}{\sqrt[]{(x^2)^2}} \\\\= \dfrac{6y\sqrt[]{y}}{x^2} \end{array} * Note that it is assumed that all variables represent positive numbers.