Найдите значения выражений: 1. a) $$\sqrt{1,44}$$; 2. a) $$\sqrt{4,2 \cdot 7,5 \cdot 14}$$; 3. a) $$\sqrt{85^2 - 84^2}$$; 6) $$\sqrt{1 \frac{11}{25}}$$; 6) $$\frac{(3\sqrt{13})^2}{52}$$; 6) $$(5+\sqrt{57})\cdot(\sqrt{57}-5)$$; B) $$\sqrt{72} \cdot \sqrt{50}$$; B) $$(7\sqrt{45}-6\sqrt{20})\cdot\sqrt{5}$$; г) $$\sqrt{2^8} \cdot 3$$.

Решение:

1. 1. a) \(\sqrt{1,44} = \sqrt{\frac{144}{100}} = \frac{\sqrt{144}}{\sqrt{100}} = \frac{12}{10} = 1,2\)
2. 2. a) \(\sqrt{4,2 \cdot 7,5 \cdot 14} = \sqrt{\frac{42}{10} \cdot \frac{75}{10} \cdot 14} = \sqrt{\frac{21}{5} \cdot \frac{15}{2} \cdot 14} = \sqrt{\frac{21 \cdot 3 \cdot 14}{2}} = \sqrt{21 \cdot 3 \cdot 7} = \sqrt{3 \cdot 7 \cdot 3 \cdot 7} = \sqrt{3^2 \cdot 7^2} = 3 \cdot 7 = 21\)
3. 3. a) \(\sqrt{85^2 - 84^2} = \sqrt{(85-84)(85+84)} = \sqrt{1 \cdot 169} = \sqrt{169} = 13\)
4. 6) \(\sqrt{1 \frac{11}{25}} = \sqrt{\frac{25+11}{25}} = \sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5} = 1,2\)
5. 6) \(\frac{(3\sqrt{13})^2}{52} = \frac{9 \cdot 13}{52} = \frac{9 \cdot 13}{4 \cdot 13} = \frac{9}{4} = 2,25\)
6. 6) \((5+\sqrt{57})\cdot(\sqrt{57}-5) = (\sqrt{57}+5)(\sqrt{57}-5) = (\sqrt{57})^2 - 5^2 = 57 - 25 = 32\)
7. B) \(\sqrt{72} \cdot \sqrt{50} = \sqrt{72 \cdot 50} = \sqrt{3600} = 60\)
8. B) \((7\sqrt{45}-6\sqrt{20})\cdot\sqrt{5} = (7\sqrt{9 \cdot 5}-6\sqrt{4 \cdot 5})\cdot\sqrt{5} = (7\cdot3\sqrt{5}-6\cdot2\sqrt{5})\cdot\sqrt{5} = (21\sqrt{5}-12\sqrt{5})\cdot\sqrt{5} = 9\sqrt{5}\cdot\sqrt{5} = 9\cdot5 = 45\)
9. г) \(\sqrt{2^8} \cdot 3 = 2^{8/2} \cdot 3 = 2^4 \cdot 3 = 16 \cdot 3 = 48\)

Ответ: 1.2; 21; 13; 1.2; 2.25; 32; 60; 45; 48.