Answer
$\dfrac{x\sqrt {3xy}}{{y}}$
Work Step by Step
To eliminate the radical in the denominator, we need to multiply both numerator and denominator by the denominator:
$\dfrac{\sqrt {36x^3}}{\sqrt {12y}} \times \dfrac{\sqrt {12y}}{\sqrt {12y}}$
Multiply radicals in the numerator and denominator:
$\dfrac{\sqrt {(36x^3)(12y)}}{({\sqrt {12y})(\sqrt {12y})}}$
Write each radicand 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:
$\dfrac{\sqrt {(6^2)(x^2)(x)(2^2)(3)(y)}}{{\sqrt {(12^2)(y^2)}}}$
We can now take out all the squares from under the radical sign:
$\dfrac{(6)(2)(x)\sqrt {3xy}}{{12y}}$
Multiply the coefficients together to simplify:
$\dfrac{12x\sqrt {3xy}}{{12y}}$
We can divide numerator and denominator by $12$ to simplify:
$\dfrac{x\sqrt {3xy}}{{y}}$
