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

$5x\sqrt{2x}$
Using $\sqrt{\dfrac{x}{y}}=\dfrac{\sqrt{x}}{\sqrt{y}}$ or the quotient rule of radicals, the given expression, $\dfrac{\sqrt{150x^4}}{\sqrt{3x}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{150x^4}{3x}} \\\\= \sqrt{\dfrac{50x^3\cdot\cancel{3x}}{\cancel{3x}}} \\\\= \sqrt{50x^3} \\\\= \sqrt{25x^2\cdot2x} \\\\= \sqrt{(5x)^2\cdot2x} \\\\= 5x\sqrt{2x} .\end{array} Note that variables are assumed to have positive real numbers.