Answer
$6\sqrt {2b}$
Work Step by Step
We don't want to leave radicals in the denominator, so to get rid of radicals in the denominator, we multiply both the numerator and denominator by the denominator:
$\frac{12\sqrt {3ab}}{\sqrt {6a}} • \frac{\sqrt {6a}}{\sqrt {6a}}$
Multiply to simplify:
$\frac{12\sqrt {18a^2b}}{\sqrt {36a^2}}$
Rewrite radicands as the product of two factors. One of the factors should be a perfect square so we can take its square root to remove it from under the radical sign:
$\frac{12\sqrt {3^2 • 2 • a^2 • b}}{\sqrt {6^2 • a^2}}$
Take the square root of any perfect squares:
$\frac{12 • 3 • a\sqrt {2b}}{6a}$
Multiply coefficients:
$\frac{36a\sqrt {2b}}{6a}$
Divide numerator and denominator by any factors common to both:
$6\sqrt {2b}$