Задание 3 Вычислите, используя свойства: a) √36-49;324 1,96-4; √3-√12: √18.√72: 15 16 25 15 16 √6 9,8 √27000 √48 6) √150 0.2 3000 V108 2 8) √√14; √62 +82: √(-11)2

Задание 3

Вычислите, используя свойства:

a) $$√36 \cdot 49; \sqrt{324} \cdot 1,96 \cdot 4; √3 \cdot √12; \sqrt{18} \cdot \sqrt{72}$$

1. $$√36 \cdot 49 = √36 \cdot √49 = 6 \cdot 7 = 42$$
2. $$\sqrt{324} \cdot 1,96 \cdot 4 = 18 \cdot 1,4 \cdot 2 = 50,4$$
3. $$√3 \cdot √12 = √{3 \cdot 12} = √36 = 6$$
4. $$\sqrt{18} \cdot \sqrt{72} = √{18 \cdot 72} = √{1296} = 36$$

Ответ: 42; 50,4; 6; 36

б) $$\frac{\sqrt{6}}{\sqrt{150}}; \frac{\sqrt{9,8}}{\sqrt{0,2}}; \frac{\sqrt{27000}}{\sqrt{3000}}; \frac{\sqrt{\frac{15}{16}}}{\sqrt{\frac{25}{48}}}$$

1. $$\frac{\sqrt{6}}{\sqrt{150}} = \sqrt{\frac{6}{150}} = \sqrt{\frac{1}{25}} = \frac{1}{5} = 0,2$$
2. $$\frac{\sqrt{9,8}}{\sqrt{0,2}} = \sqrt{\frac{9,8}{0,2}} = \sqrt{49} = 7$$
3. $$\frac{\sqrt{27000}}{\sqrt{3000}} = \sqrt{\frac{27000}{3000}} = \sqrt{9} = 3$$
4. $$\frac{\sqrt{\frac{15}{16}}}{\sqrt{\frac{25}{48}}} = \sqrt{\frac{\frac{15}{16}}{\frac{25}{48}}} = \sqrt{\frac{15}{16} \cdot \frac{48}{25}} = \sqrt{\frac{15 \cdot 48}{16 \cdot 25}} = \sqrt{\frac{3 \cdot 3}{1 \cdot 5}} = \sqrt{\frac{9}{5}} = \frac{3}{\sqrt{5}} = \frac{3 \sqrt{5}}{5}$$

Ответ: 0,2; 7; 3; $$\frac{3 \sqrt{5}}{5}$$

в) $$√{\sqrt{14}}; \sqrt{6^2 + 8^2}; \sqrt{(-11)^2}$$

1. $$√{\sqrt{14}} = \sqrt[4]{14}$$
2. $$\sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10$$
3. $$\sqrt{(-11)^2} = |-11| = 11$$

Ответ: $$\sqrt[4]{14}$$; 10; 11