Answer
$\frac{2\sqrt {5ab}}{5a}$
Work Step by Step
First, we need to cancel out common terms in the numerator and denominator:
$\sqrt {\frac{4b}{5a}}$
Separate the radical:
$\frac{\sqrt {4b}}{\sqrt {5a}}$
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:
$\frac{\sqrt {4b}}{\sqrt {5a}} • \frac{\sqrt {5a}}{\sqrt {5a}}$
Multiply to simplify:
$\frac{\sqrt {4b • 5a}}{\sqrt {5a • 5a}}$
Perform the multiplication:
$\frac{\sqrt {20ab}}{\sqrt {25a^2}}$
Rewrite radicands to separate out perfect squares:
$\frac{\sqrt {4 • 5 • ab}}{\sqrt {25 • a^2}}$
Take the square root of any perfect squares:
$\frac{2\sqrt {5ab}}{5a}$