Answer
$\dfrac{y\sqrt{15xy}}{6x^2}$
Work Step by Step
Multiplying the numerator and the denominator of the given expression, $
\dfrac{\sqrt{5y^3}}{\sqrt{12x^3}}
,$ by $
\sqrt{3x}
$ results to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{5y^3}}{\sqrt{12x^3}}\cdot\dfrac{\sqrt{3x}}{\sqrt{3x}}
\\\\=
\dfrac{\sqrt{5y^3(3x)}}{\sqrt{12x^3(3x)}}
\\\\=
\dfrac{\sqrt{15xy^3}}{\sqrt{36x^4}}
\\\\=
\dfrac{\sqrt{y^2\cdot15xy}}{\sqrt{(6x^2)^2}}
\\\\=
\dfrac{y\sqrt{15xy}}{6x^2}
.\end{array}
