3. Найдите значение произведения:

Решение:

1. a) \( \sqrt{2} \cdot \sqrt{118} = \sqrt{2 \cdot 118} = \sqrt{236} \)

   б) \( \sqrt{3} \cdot \sqrt{48} = \sqrt{3 \cdot 48} = \sqrt{144} = 12 \)

   в) \( \sqrt{13} \cdot \sqrt{52} = \sqrt{13 \cdot 52} = \sqrt{13 \cdot 13 \cdot 4} = \sqrt{169 \cdot 4} = 13 \cdot 2 = 26 \)

   г) \( \sqrt{12} \cdot \sqrt{75} = \sqrt{12 \cdot 75} = \sqrt{900} = 30 \)

2. a) \( \sqrt{4,5} \cdot \sqrt{172} = \sqrt{\frac{45}{10}} \cdot \sqrt{172} = \sqrt{\frac{9}{2}} \cdot \sqrt{172} = \sqrt{\frac{9 \cdot 172}{2}} = \sqrt{9 \cdot 86} = 3 \sqrt{86} \)

   б) \( \sqrt{12,5} \cdot \sqrt{198} = \sqrt{\frac{125}{10}} \cdot \sqrt{198} = \sqrt{\frac{25}{2}} \cdot \sqrt{198} = \sqrt{\frac{25 \cdot 198}{2}} = \sqrt{25 \cdot 99} = 5 \sqrt{99} = 5 \cdot 3 \sqrt{11} = 15 \sqrt{11} \)

   в) \( \sqrt{0,4} \cdot \sqrt{3,6} = \sqrt{\frac{4}{10}} \cdot \sqrt{\frac{36}{10}} = \sqrt{\frac{4 \cdot 36}{100}} = \frac{2 \cdot 6}{10} = \frac{12}{10} = 1,2 \)

   г) \( \sqrt{200} \cdot \sqrt{0,18} = \sqrt{200 \cdot \frac{18}{100}} = \sqrt{2 \cdot 18} = \sqrt{36} = 6 \)

3. a) \( \sqrt{\frac{11}{13}} \cdot \sqrt{\frac{13}{25}} = \sqrt{\frac{11 \cdot 13}{13 \cdot 25}} = \sqrt{\frac{11}{25}} = \frac{\sqrt{11}}{5} \)

   б) \( \sqrt{\frac{3}{7}} \cdot \sqrt{\frac{7}{11}} = \sqrt{\frac{3 \cdot 7}{7 \cdot 11}} = \sqrt{\frac{3}{11}} \)

Ответ: 1) a) \(\sqrt{236}\), б) 12, в) 26, г) 30; 2) a) \(3\sqrt{86}\), б) \(15\sqrt{11}\), в) 1,2, г) 6; 3) a) \(\frac{\sqrt{11}}{5}\), б) \(\sqrt{\frac{3}{11}}\).