Answer
$2\sqrt{6}$
Work Step by Step
$\bf{\text{Solution Outline:}}$
To rationalize the given radical expression, $
\dfrac{12}{\sqrt{6}}
,$ 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{12}{\sqrt{6}}\cdot\dfrac{\sqrt{6}}{\sqrt{6}}
\\\\=
\dfrac{12\sqrt{6}}{\sqrt{6}\sqrt{6}}
.\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{12\sqrt{6}}{\sqrt{6(6)}}
\\\\=
\dfrac{12\sqrt{6}}{\sqrt{6^2}}
\\\\=
\dfrac{12\sqrt{6}}{6}
\\\\=
\dfrac{\cancel{6}(2)\sqrt{6}}{\cancel{6}}
\\\\=
2\sqrt{6}
.\end{array}
