## Intermediate Algebra (12th Edition)

$\dfrac{8}{5}$
$\bf{\text{Solution Outline:}}$ To simplify the given radical expression, $\dfrac{16\sqrt{3}}{5\sqrt{12}} ,$ use the laws of radicals. Then extract the root of the factor that is a perfect power of the index $\bf{\text{Solution Details:}}$ Using the Quotient Rule of radicals which is given by $\sqrt[n]{\dfrac{x}{y}}=\dfrac{\sqrt[n]{x}}{\sqrt[n]{y}}{},$ the expression above is equivalent to \begin{array}{l}\require{cancel} \dfrac{16}{5}\sqrt{\dfrac{3}{12}} \\\\= \dfrac{16}{5}\sqrt{\dfrac{1}{4}} \\\\= \dfrac{16}{5}\sqrt{\left( \dfrac{1}{2} \right)^2} \\\\= \dfrac{16}{5}\cdot\dfrac{1}{2} \\\\= \dfrac{\cancel{2}(8)}{5}\cdot\dfrac{1}{\cancel{2}} \\\\= \dfrac{8}{5} .\end{array}