Answer
$\frac{5}{9}$
Work Step by Step
According to the textbook, a number, $a$, is a square root of another number, $b$, if $a^2=b$.
$(\frac{5}{9})^2=\frac{25}{81}$, so $\frac{5}{9}$ is a square root of $\frac{25}{81}$.
Therefore: $\sqrt {\frac{25}{81}}=\frac{5}{9}$