Answer
$\dfrac{\sqrt{3x}}{6}$
Work Step by Step
Multiplying both the numerator and the denominator by a factor that will make the denominator a perfect power of the radical, the rationalized-denominator form of the given expression, $
\sqrt{\dfrac{x}{12}}
,$ is
\begin{array}{l}\require{cancel}
\sqrt{\dfrac{x}{12}\cdot\dfrac{3}{3}}
\\\\=
\sqrt{\dfrac{3x}{36}}
\\\\=
\sqrt{\dfrac{3x}{(6)^2}}
\\\\=
\dfrac{\sqrt{3x}}{6}
.\end{array}
Note that all variables are assumed to have positive real numbers.