Answer
$\dfrac{x\sqrt{15}}{5y}$
Work Step by Step
Using the properties of radicals, the given expression, $
\dfrac{\sqrt{3x^2}}{\sqrt{5y^2}}
,$ simplifies to
\begin{array}{l}\require{cancel}
\dfrac{\sqrt{x^2\cdot3}}{\sqrt{y^2\cdot5}}
\\\\=
\dfrac{\sqrt{(x)^2\cdot3}}{\sqrt{(y)^2\cdot5}}
\\\\=
\dfrac{x\sqrt{3}}{y\sqrt{5}}
\\\\=
\dfrac{x\sqrt{3}}{y\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}
\\\\=
\dfrac{x\sqrt{15}}{y\cdot5}
\\\\=
\dfrac{x\sqrt{15}}{5y}
.\end{array}
Note that all variables are assumed to represent positive real numbers.
