#### Answer

$\dfrac{9\sqrt{15}}{5}$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{9\sqrt{3}}{\sqrt{5}}
,$ multiply both the numerator and the denominator by an expression that will make the denominator a perfect power of the index.
$\bf{\text{Solution Details:}}$
Multiplying both the numerator and the denominator by an expression that will make the denominator a perfect power of the index results to
\begin{array}{l}\require{cancel}
\dfrac{9\sqrt{3}}{\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}
.\end{array}
Using the Product Rule of radicals which is given by $\sqrt[m]{x}\cdot\sqrt[m]{y}=\sqrt[m]{xy},$ the expression above is equivalent to
\begin{array}{l}\require{cancel}
\dfrac{9\sqrt{3(5)}}{\sqrt{5(5)}}
\\\\=
\dfrac{9\sqrt{15}}{\sqrt{5^2}}
\\\\=
\dfrac{9\sqrt{15}}{5}
.\end{array}