Вычислить (343-346). 343 1) √2·√32; 2) √10·√90; 3) √3·√7·√21; 4) √2·√22·√11; 5) √\frac{1}{2}·√\frac{2}{3}·√3; 6) √\frac{2}{5}·√\frac{5}{7}·√\frac{7}{8}

343

1. $$\sqrt{2} \cdot \sqrt{32} = \sqrt{2 \cdot 32} = \sqrt{64} = 8$$

   Ответ: 8

2. $$\sqrt{10} \cdot \sqrt{90} = \sqrt{10 \cdot 90} = \sqrt{900} = 30$$

   Ответ: 30

3. $$\sqrt{3} \cdot \sqrt{7} \cdot \sqrt{21} = \sqrt{3 \cdot 7 \cdot 21} = \sqrt{3 \cdot 7 \cdot 3 \cdot 7} = \sqrt{3^2 \cdot 7^2} = 3 \cdot 7 = 21$$

   Ответ: 21

4. $$\sqrt{2} \cdot \sqrt{22} \cdot \sqrt{11} = \sqrt{2 \cdot 22 \cdot 11} = \sqrt{2 \cdot 2 \cdot 11 \cdot 11} = \sqrt{2^2 \cdot 11^2} = 2 \cdot 11 = 22$$

   Ответ: 22

5. $$\sqrt{\frac{1}{2}} \cdot \sqrt{\frac{2}{3}} \cdot \sqrt{3} = \sqrt{\frac{1}{2} \cdot \frac{2}{3} \cdot 3} = \sqrt{\frac{1 \cdot 2 \cdot 3}{2 \cdot 3}} = \sqrt{1} = 1$$

   Ответ: 1

6. $$\sqrt{\frac{2}{5}} \cdot \sqrt{\frac{5}{7}} \cdot \sqrt{\frac{7}{8}} = \sqrt{\frac{2}{5} \cdot \frac{5}{7} \cdot \frac{7}{8}} = \sqrt{\frac{2 \cdot 5 \cdot 7}{5 \cdot 7 \cdot 8}} = \sqrt{\frac{2}{8}} = \sqrt{\frac{1}{4}} = \frac{1}{2}$$

   Ответ: 1/2