6) \( \sqrt{\frac{400}{10000 \cdot 121}} \)

\( 400 = 20^2, \; 10000 = 100^2, \; 121 = 11^2 \)\( \Rightarrow \sqrt{\frac{400}{10000 \cdot 121}} = \sqrt{\frac{20^2}{100^2 \cdot 11^2}} = \frac{20}{100 \cdot 11} = \frac{20}{1100} = \frac{2}{110} = \frac{1}{55} \). Ответ: \( \frac{1}{55} \).