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

$2b\sqrt{2b}$
Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression, $\dfrac{\sqrt{56ab^3}}{\sqrt{7a}} ,$ is equivalent to \begin{array}{l}\require{cancel} \dfrac{\sqrt{56ab^3}}{\sqrt{7a}} \\\\= \sqrt{\dfrac{56ab^3}{7a}} \\\\= \sqrt{8b^3} .\end{array} Extracting the factor that is a perfect power of the index results to \begin{array}{l}\require{cancel} \sqrt{8b^3} \\\\= \sqrt{4b^2\cdot2b} \\\\= \sqrt{(2b)^2\cdot2b} \\\\= 2b\sqrt{2b} .\end{array} Note that all variables are assumed to be positive.