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

$10x\sqrt{2x}$
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $\dfrac{\sqrt{400x^4}}{\sqrt{2x}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{400x^4}{2x}} \\\\= \sqrt{\dfrac{200x^3\cdot\cancel{2x}}{\cancel{2x}}} \\\\= \sqrt{200x^3} \\\\= \sqrt{100x^2\cdot2x} \\\\= \sqrt{(10x)^2\cdot2x} \\\\= 10x\sqrt{2x} .\end{array} Note that variables are assumed to have positive real numbers.