\[\boxed{\text{366.}\text{\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
Пояснение.
Если \(a \geq 0\ и\ b \geq 0,\ \)то:
\[\sqrt{\text{ab}} = \sqrt{a} \cdot \sqrt{b}.\]
Если \(a \geq 0\ и\ b > 0\), то:
\[\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}.\]
Решение.
\[\textbf{а)}\ \sqrt{0,04 \cdot 81 \cdot 25} = 0,2 \cdot 9 \cdot 5 =\]
\[= 9\]
\[\textbf{б)}\ \sqrt{0,09 \cdot 16 \cdot 0,04} =\]
\[= 0,3 \cdot 4 \cdot 0,2 = 0,24\]
\[\textbf{в)}\ \sqrt{1\frac{7}{9} \cdot \frac{4}{25}} = \sqrt{\frac{16}{9} \cdot \frac{4}{25}} =\]
\[= \frac{4}{3} \cdot \frac{2}{5} = \frac{8}{15}\]
\[\textbf{г)}\ \sqrt{\frac{121}{144} \cdot 2\frac{1}{4}} = \sqrt{\frac{121}{144} \cdot \frac{9}{4}} =\]
\[= \frac{11}{12} \cdot \frac{3}{2} = \frac{33}{24} = 1\frac{9}{24} = 1\frac{3}{8}\ \]