## Introductory Algebra for College Students (7th Edition)

$\sqrt{(2x)^2}$
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $\dfrac{\sqrt{32x^3}}{\sqrt{8x}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{32x^3}{8x}} \\\\= \sqrt{\dfrac{4x^2\cdot\cancel{8x}}{\cancel{8x}}} \\\\= \sqrt{4x^2} \\\\= \sqrt{(2x)^2} .\end{array} Note that variables are assumed to have positive real numbers.