Answer
$\dfrac{x^3}{2\sqrt{3x}}$
Work Step by Step
Rationalizing the numerator of $
\dfrac{\sqrt{3x^5}}{6}
$ results to
\begin{array}{l}
\dfrac{\sqrt{x^4\cdot3x}}{6}
\\\\=
\dfrac{x^2\sqrt{3x}}{6}
\\\\=
\dfrac{x^2\sqrt{3x}}{6}
\cdot
\dfrac{\sqrt{3x}}{\sqrt{3x}}
\\\\=
\dfrac{x^2\sqrt{9x^2}}{6\sqrt{3x}}
\\\\=
\dfrac{x^2\cdot3x}{6\sqrt{3x}}
\\\\=
\dfrac{3x^3}{6\sqrt{3x}}
\\\\=
\dfrac{x^3}{2\sqrt{3x}}
.\end{array}