Answer
$-\dfrac{4\sqrt{3}}{3}$
Work Step by Step
Getting the factor that is a perfect root of the index, the given expression, $
-\sqrt{\dfrac{16}{3}}
,$ simplifies to
\begin{array}{l}\require{cancel}
-\sqrt{16\cdot\dfrac{1}{3}}
\\\\=
-\sqrt{(4)^2\cdot\dfrac{1}{3}}
\\\\=
-4\sqrt{\dfrac{1}{3}}
.\end{array}
Rationalizing the denominator results to
\begin{array}{l}\require{cancel}
-4\sqrt{\dfrac{1}{3}\cdot\dfrac{3}{3}}
\\\\=
-4\sqrt{\dfrac{3}{(3)^2}}
\\\\=
-4\cdot\dfrac{\sqrt{3}}{\sqrt{(3)^2}}
\\\\=
-4\cdot\dfrac{\sqrt{3}}{3}
\\\\=
-\dfrac{4\sqrt{3}}{3}
.\end{array}
