1. Найдите значение выражения: а) \(\sqrt{36\cdot1{,}69}\); \(\sqrt{4\frac{29}{49}}\); \(2\sqrt{(-64)^2}\); б) \(\sqrt{48}\cdot\sqrt{3}\); \(\frac{\sqrt{7}}{\sqrt{175}}\); \(\sqrt{2^6\cdot5^2}\).

а)

1. \(\sqrt{36\cdot1.69}=\sqrt{60.84}=7.8\).
2. \(4\frac{29}{49}=\frac{225}{49}\), поэтому \(\sqrt{4\frac{29}{49}}=\sqrt{\frac{225}{49}}=\frac{15}{7}\).
3. \(2\sqrt{(-64)^2}=2\cdot|-64|=128\).

б)

1. \(\sqrt{48}\cdot\sqrt{3}=\sqrt{144}=12\).
2. \(\frac{\sqrt{7}}{\sqrt{175}}=\sqrt{\frac{7}{175}}=\sqrt{\frac{1}{25}}=\frac{1}{5}\).
3. \(\sqrt{2^6\cdot5^2}=\sqrt{64\cdot25}=\sqrt{1600}=40\).

Ответ: а) 7,8; \(\frac{15}{7}\); 128. б) 12; \(\frac{1}{5}\); 40.