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{12x^3}
$ results to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{5y^3}}{\sqrt{12x^3}}\cdot\dfrac{\sqrt{12x^3}}{\sqrt{12x^3}}
\\\\=
\dfrac{\sqrt{5y^3(12x^3)}}{\sqrt{12x^3(12x^3)}}
\\\\=
\dfrac{\sqrt{60x^3y^3}}{\sqrt{(12x^3)^2}}
\\\\=
\dfrac{\sqrt{4x^2y^2\cdot15xy}}{\sqrt{(12x^3)^2}}
\\\\=
\dfrac{2xy\sqrt{15xy}}{12x^3}
\\\\=
\dfrac{\cancel{2x}y\sqrt{15xy}}{\cancel{2x}\cdot6x^2}
\\\\=
\dfrac{y\sqrt{15xy}}{6x^2}
.\end{array}
