Решение заданий:

Задание 1

1. a) $$\sqrt{1,44} = \sqrt{\frac{144}{100}} = \frac{\sqrt{144}}{\sqrt{100}} = \frac{12}{10} = 1,2$$

2. б) $$\sqrt{1\frac{11}{25}} = \sqrt{\frac{1 \cdot 25 + 11}{25}} = \sqrt{\frac{36}{25}} = \frac{\sqrt{36}}{\sqrt{25}} = \frac{6}{5} = 1,2$$

3. в) $$\sqrt{72} \cdot \sqrt{50} = \sqrt{72 \cdot 50} = \sqrt{3600} = 60$$

4. г) $$\sqrt{2^8 \cdot 3^6} = \sqrt{2^8} \cdot \sqrt{3^6} = 2^{\frac{8}{2}} \cdot 3^{\frac{6}{2}} = 2^4 \cdot 3^3 = 16 \cdot 27 = 432$$

Задание 2

1. a) $$\sqrt{4,2 \cdot 7,5 \cdot 14} = \sqrt{\frac{42}{10} \cdot \frac{75}{10} \cdot 14} = \sqrt{\frac{21}{5} \cdot \frac{15}{2} \cdot 14} = \sqrt{\frac{21 \cdot 15 \cdot 14}{5 \cdot 2}} = \sqrt{21 \cdot 3 \cdot 14} = \sqrt{21 \cdot 42} = \sqrt{21 \cdot 21 \cdot 2} = 21\sqrt{2}$$

2. б) $$\frac{(3\sqrt{13})^2}{52} = \frac{3^2 \cdot (\sqrt{13})^2}{52} = \frac{9 \cdot 13}{52} = \frac{9 \cdot 13}{4 \cdot 13} = \frac{9}{4} = 2,25$$

Задание 3

1. a) $$\sqrt{85^2 - 84^2} = \sqrt{(85 - 84)(85 + 84)} = \sqrt{1 \cdot 169} = \sqrt{169} = 13$$

2. б) $$(5 + \sqrt{57})(\sqrt{57} - 5) = (\sqrt{57})^2 - 5^2 = 57 - 25 = 32$$

3. в) $$(7\sqrt{45} - 6\sqrt{20}) \cdot \sqrt{5} = (7\sqrt{9 \cdot 5} - 6\sqrt{4 \cdot 5}) \cdot \sqrt{5} = (7 \cdot 3\sqrt{5} - 6 \cdot 2\sqrt{5}) \cdot \sqrt{5} = (21\sqrt{5} - 12\sqrt{5}) \cdot \sqrt{5} = 9\sqrt{5} \cdot \sqrt{5} = 9 \cdot 5 = 45$$

Ответ:

Задание 1: a) 1,2; б) 1,2; в) 60; г) 432.

Задание 2: a) $$21\sqrt{2}$$; б) 2,25.

Задание 3: a) 13; б) 32; в) 45.