#### Answer

$\dfrac{p\sqrt{p+2}}{p+2}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the denominator of the given expression, $
\dfrac{p}{\sqrt{p+2}}
,$ multiply both the numerator and the denominator by the denominator.
$\bf{\text{Solution Details:}}$
Multiplying both the numerator and the denominator by the denominator, the given expression is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{p}{\sqrt{p+2}}\cdot\dfrac{\sqrt{p+2}}{\sqrt{p+2}}
\\\\=
\dfrac{p\sqrt{p+2}}{(\sqrt{p+2})^2}
\\\\=
\dfrac{p\sqrt{p+2}}{p+2}
.\end{array}