Skills Handbook - Squaring Numbers and Finding Square Roots - Exercises - Page 889: 12

$\frac{7}{9}$

To find out the square root of a number, we must find the number whose square is the original number. To find the square root of a fraction, we find the square root of the numerator and the denominator. Therefore, $\sqrt {\frac{49}{81}}=\frac{\sqrt {49}}{\sqrt {81}}=\frac{7}{9}$, because $(\frac{7}{9})^2=\frac{49}{81}$.