21. \( \sqrt{\frac{169}{441}} \) 22. \( \left(\frac{5}{6}+\frac{4}{9}\right) \cdot 8 \) 23. \( \frac{8}{9} \div \frac{4}{15} \) 24. \( \sqrt{\frac{80}{5}} \) 25. \( \sqrt{\frac{81}{100}}-3 \cdot \frac{2}{15} \)

1. Compute the square root of the fraction: \[ \sqrt{\frac{169}{441}} = \frac{\sqrt{169}}{\sqrt{441}} = \frac{13}{21}. \] 2. First add the fractions and then multiply by 8: \[ \frac{5}{6}+\frac{4}{9} = \frac{15}{18}+\frac{8}{18} = \frac{23}{18}. \] Multiplying by 8: \[ \left(\frac{23}{18}\right)\cdot 8 = \frac{23 \cdot 8}{18} = \frac{184}{18} = \frac{92}{9}. \] 3. Divide the fractions by multiplying by the reciprocal: \[ \frac{8}{9} \div \frac{4}{15} = \frac{8}{9}\cdot \frac{15}{4} = \frac{8\cdot15}{9\cdot4} = \frac{120}{36} = \frac{10}{3}. \] 4. Simplify the expression under the square root first: \[ \sqrt{\frac{80}{5}} = \sqrt{16} = 4. \] 5. Compute the square root and then subtract: \[ \sqrt{\frac{81}{100}} = \frac{9}{10}. \] Next, compute the other term: \[ 3\cdot \frac{2}{15} = \frac{6}{15} = \frac{2}{5}. \] Finally, subtract: \[ \frac{9}{10} - \frac{2}{5} = \frac{9}{10} - \frac{4}{10} = \frac{5}{10} = \frac{1}{2}. \]