Answer
$5\sqrt{3}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{15}{\sqrt{3}}
,$ 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{15}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}
\\\\=
\dfrac{15\sqrt{3}}{\sqrt{3}\sqrt{3}}
.\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{15\sqrt{3}}{\sqrt{3(3)}}
\\\\=
\dfrac{15\sqrt{3}}{\sqrt{3^2}}
\\\\=
\dfrac{15\sqrt{3}}{3}
\\\\=
\dfrac{\cancel{3}(5)\sqrt{3}}{\cancel{3}}
\\\\=
5\sqrt{3}
.\end{array}
