## Elementary Algebra

$\dfrac{2\sqrt{3}}{x}$
Using the properties of radicals, the given expression, $\sqrt{\dfrac{12}{x^2}} ,$ simplifies to \begin{array}{l}\require{cancel} \sqrt{\dfrac{4}{x^2}\cdot3} \\\\= \sqrt{\left(\dfrac{2}{x}\right)^2\cdot3} \\\\= \dfrac{2}{x}\sqrt{3} \\\\= \dfrac{2\sqrt{3}}{x} .\end{array} Note that all variables are assumed to represent positive real numbers.