Answer
a) $y\sqrt {15xy}/6x^2$
b) $y\sqrt {15xy}/6x^2$
c) There are multiple expressions by which the numerator and denominator can be rationalized and which result in the same result.
Work Step by Step
$\sqrt {5y^3}\sqrt {12x^3}/(\sqrt {12x^3}\sqrt {12x^3})$
a)
$\sqrt {5y^3}/\sqrt {12x^3}$
$(\sqrt {5y^3})(\sqrt {12x^3})/(\sqrt {12x^3})(\sqrt {12x^3})$
$(\sqrt {5y^3})(\sqrt {12x^3})/(\sqrt {12x^3})(\sqrt {12x^3})$
$(\sqrt {5y^3})(\sqrt {12x^3})/12x^3$
$(\sqrt {5*12*x^3*y^3})/12x^3$
$(\sqrt {5*3*4*x^2*x*y^2*y})/12x^3$
$2xy(\sqrt {5*3*x*y})/12x^3$
$y/6x^2(\sqrt {5*3*x*y})$
$y/6x^2(\sqrt {15xy})$
b)
$(\sqrt {5y^3})/(\sqrt {12x^3})$
$(\sqrt {5y^3})(\sqrt {3x})/(\sqrt {12x^3})(\sqrt {3x})$
$(\sqrt {15xy^3})/(\sqrt {36x^4})$
$(\sqrt {15xy^2*y})/(\sqrt {(6x^2)^2})$
$\frac{y}{6x^2}*\sqrt {15xy}$
