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

$6x$
Using $\sqrt{x}\cdot\sqrt{y}=\sqrt{xy}$ or the product rule of radicals, the given expression, $\sqrt{12x}\cdot\sqrt{3x} ,$ is equivalent to \begin{array}{l}\require{cancel} \sqrt{12x(3x)} \\\\= \sqrt{36x^2} \\\\= \sqrt{(6x)^2} \\\\= 6x .\end{array} Note that variables are assumed to have positive real numbers.