Answer
$\dfrac{8}{5}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
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}
