Answer
$\dfrac{\sqrt{15p}}{3p}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
Use the laws of radicals to simplify the given expression, $
\sqrt{\dfrac{5}{3p}}
.$ Then rationalize the denominator.
$\bf{\text{Solution Details:}}$
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{\sqrt{5}}{\sqrt{3p}}
.\end{array}
Rationalizing the denominator results to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{5}}{\sqrt{3p}}\cdot\dfrac{\sqrt{3p}}{\sqrt{3p}}
\\\\=
\dfrac{\sqrt{5(3p)}}{(\sqrt{3p})^2} \text{ (product rule)}
\\\\=
\dfrac{\sqrt{15p}}{3p}
.\end{array}
