5. Сравните числа: 1) 3√7 и 4√6; 2) 5√√140.

5. Сравните числа:

1. $$3\sqrt{7} \text{ и } 4\sqrt{6}$$ $$(3\sqrt{7})^2 = 9 \cdot 7 = 63$$ $$(4\sqrt{6})^2 = 16 \cdot 6 = 96$$ $$63 < 96$$ $$3\sqrt{7} < 4\sqrt{6}$$

   Ответ: $$3\sqrt{7} < 4\sqrt{6}$$

2. $$5\sqrt{\frac{7}{5}} \text{ и } \frac{1}{2}\sqrt{140}$$ $$(5\sqrt{\frac{7}{5}})^2 = 25 \cdot \frac{7}{5} = 5 \cdot 7 = 35$$ $$(\frac{1}{2}\sqrt{140})^2 = \frac{1}{4} \cdot 140 = 35$$ $$35 = 35$$ $$5\sqrt{\frac{7}{5}} = \frac{1}{2}\sqrt{140}$$

   Ответ: $$5\sqrt{\frac{7}{5}} = \frac{1}{2}\sqrt{140}$$