#### Answer

$\dfrac{5\sqrt{2}}{3}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To simplify the given radical expression, $
\dfrac{\sqrt{32}}{3}+\dfrac{2\sqrt{2}}{3}-\dfrac{\sqrt{2}}{\sqrt{9}}
,$ find a factor of the radicand that is a perfect power of the index. Then, extract the root of that factor. Finally, combine the like radicals.
$\bf{\text{Solution Details:}}$
Rewriting the radicand with a factor that is a perfect power of the index, the given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{16\cdot2}}{3}+\dfrac{2\sqrt{2}}{3}-\dfrac{\sqrt{2}}{\sqrt{9}}
\\\\=
\dfrac{\sqrt{(4)^2\cdot2}}{3}+\dfrac{2\sqrt{2}}{3}-\dfrac{\sqrt{2}}{\sqrt{(3)^2}}
.\end{array}
Extracting the root of the factor that is a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{4\sqrt{2}}{3}+\dfrac{2\sqrt{2}}{3}-\dfrac{\sqrt{2}}{3}
.\end{array}
Combining the like radicals results to
\begin{array}{l}\require{cancel}
\dfrac{4\sqrt{2}+2\sqrt{2}-\sqrt{2}}{3}
\\\\=
\dfrac{5\sqrt{2}}{3}
.\end{array}