33. Вычислите: 1) \(\sqrt{\frac{9}{100}}\) 2) \(\sqrt{\frac{100}{49}}\) 7) \(\sqrt{\frac{25}{64}} + \sqrt{\frac{49}{144}}\) 13) \(\sqrt{64 \cdot 49} \cdot \sqrt{196 \cdot 324}\) 8) \(\sqrt{\frac{16}{81}} - \sqrt{\frac{169}{225}}\) 14) \(5\sqrt{\frac{4}{9}} - 11\sqrt{\frac{14}{25}}\)

Решение:

1. \(\sqrt{\frac{9}{100}} = \frac{\sqrt{9}}{\sqrt{100}} = \frac{3}{10}\)
2. \(\sqrt{\frac{100}{49}} = \frac{\sqrt{100}}{\sqrt{49}} = \frac{10}{7}\)
3. \(\sqrt{\frac{25}{64}} + \sqrt{\frac{49}{144}} = \frac{\sqrt{25}}{\sqrt{64}} + \frac{\sqrt{49}}{\sqrt{144}} = \frac{5}{8} + \frac{7}{12} = \frac{5 \cdot 3}{24} + \frac{7 \cdot 2}{24} = \frac{15+14}{24} = \frac{29}{24}\)
4. \(\sqrt{64 \cdot 49} \cdot \sqrt{196 \cdot 324} = \sqrt{64} \cdot \sqrt{49} \cdot \sqrt{196} \cdot \sqrt{324} = 8 \cdot 7 \cdot 14 \cdot 18 = 56 \cdot 252 = 14112\)
5. \(\sqrt{\frac{16}{81}} - \sqrt{\frac{169}{225}} = \frac{\sqrt{16}}{\sqrt{81}} - \frac{\sqrt{169}}{\sqrt{225}} = \frac{4}{9} - \frac{13}{15} = \frac{4 \cdot 5}{45} - \frac{13 \cdot 3}{45} = \frac{20 - 39}{45} = -\frac{19}{45}\)
6. \(5\sqrt{\frac{4}{9}} - 11\sqrt{\frac{14}{25}} = 5 \cdot \frac{\sqrt{4}}{\sqrt{9}} - 11 \cdot \frac{\sqrt{14}}{\sqrt{25}} = 5 \cdot \frac{2}{3} - 11 \cdot \frac{\sqrt{14}}{5} = \frac{10}{3} - \frac{11\sqrt{14}}{5} = \frac{10 \cdot 5 - 11\sqrt{14} \cdot 3}{15} = \frac{50 - 33\sqrt{14}}{15}\)

Ответ: 1) \(\frac{3}{10}\); 2) \(\frac{10}{7}\); 7) \(\frac{29}{24}\); 13) \(14112\); 8) \(-\frac{19}{45}\); 14) \(\frac{50 - 33\sqrt{14}}{15}\).