Answer
$\dfrac{\sqrt {6xy}}{{2y}}$
Work Step by Step
To eliminate the radical in the denominator, we need to multiply both numerator and denominator by the denominator:
$\dfrac{\sqrt {3x}}{\sqrt {2y}} \times \dfrac{\sqrt {2y}}{\sqrt {2y}}$
Multiply radicals in the numerator and denominator:
$\dfrac{\sqrt {(3x)(2y)}}{{\sqrt {(2y)(2y)}}}$
Where possible, write radicands as a product of squares so that we can take the square root of the squares and take them out from under the radical sign:
$\dfrac{\sqrt {6xy}}{{\sqrt {(2^2)(y^2)}}}$
We can now take out all the squares from under the radical sign:
$\dfrac{\sqrt {6xy}}{{2y}}$
