#### Answer

$\dfrac{2\sqrt{a}}{3ab}$

#### Work Step by Step

The variables are assumed to be non-zero as they are also in the denominator.
RECALL:
$\dfrac{\sqrt{a}}{\sqrt{b}} = \sqrt{\dfrac{a}{b}}, a\ge0, b\gt0.$
Use the rule above to have
$\require{cancel}
\sqrt{\dfrac{20ab}{45a^2b^3}}
\\=\sqrt{\dfrac{\cancel{20}4a\cancel{b}}{\cancel{45}9a^2\cancel{b^3}b^2}}
\\=\sqrt{\dfrac{4a}{9a^2b^2}}
\\=\sqrt{\dfrac{2^2(a)}{(3ab)^2}}
\\=\dfrac{2}{3ab} \cdot \sqrt{a}
\\=\dfrac{2\sqrt{a}}{3ab}.$