5. Сравните числа: 1) $$3\sqrt{5}$$ и $$5\sqrt{2};$$ 2) $$4\sqrt{\frac{3}{8}}$$ и $$\frac{1}{5}\sqrt{150}$$.

a) $$3\sqrt{5}$$ и $$5\sqrt{2}$$

$$(3\sqrt{5})^2 = 9 \cdot 5 = 45$$

$$(5\sqrt{2})^2 = 25 \cdot 2 = 50$$

Так как 45 < 50, то $$3\sqrt{5} < 5\sqrt{2}$$

Ответ: $$3\sqrt{5} < 5\sqrt{2}$$

б) $$4\sqrt{\frac{3}{8}}$$ и $$\frac{1}{5}\sqrt{150}$$

$$(4\sqrt{\frac{3}{8}})^2 = 16 \cdot \frac{3}{8} = 2 \cdot 3 = 6$$

$$(\frac{1}{5}\sqrt{150})^2 = \frac{1}{25} \cdot 150 = 6$$

Так как 6 = 6, то $$4\sqrt{\frac{3}{8}} = \frac{1}{5}\sqrt{150}$$

Ответ: $$4\sqrt{\frac{3}{8}} = \frac{1}{5}\sqrt{150}$$