• 2. Сравните√60 и 10 2 1 V5.

Сравним числа $$\frac{1}{2}\sqrt{60}$$ и $$10\sqrt{\frac{1}{5}}$$.

1. $$\frac{1}{2}\sqrt{60} = \sqrt{\frac{1}{4}}\cdot \sqrt{60} = \sqrt{\frac{60}{4}} = \sqrt{15}$$
2. $$10\sqrt{\frac{1}{5}}=\sqrt{100}\cdot \sqrt{\frac{1}{5}} = \sqrt{\frac{100}{5}}=\sqrt{20}$$
3. Т.к. $$15 < 20$$, то $$\sqrt{15} < \sqrt{20}$$
4. $$\frac{1}{2}\sqrt{60} < 10\sqrt{\frac{1}{5}}$$

Ответ: $$\frac{1}{2}\sqrt{60} < 10\sqrt{\frac{1}{5}}$$