5. Сравните числа: 1) 4√3 и 3√8; 2) 4 и 750.

Сравним числа:

1. $$4\sqrt{3}$$ и $$3\sqrt{8}$$ $$(4\sqrt{3})^2 = 16 \cdot 3 = 48$$ $$(3\sqrt{8})^2 = 9 \cdot 8 = 72$$ Так как $$48 < 72$$, то $$4\sqrt{3} < 3\sqrt{8}$$.
2. $$4\sqrt{\frac{15}{8}}$$ и $$\frac{1}{5}\sqrt{750}$$ $$(4\sqrt{\frac{15}{8}})^2 = 16 \cdot \frac{15}{8} = 2 \cdot 15 = 30$$ $$(\frac{1}{5}\sqrt{750})^2 = \frac{1}{25} \cdot 750 = 30$$ Так как $$30 = 30$$, то $$4\sqrt{\frac{15}{8}} = \frac{1}{5}\sqrt{750}$$.

Ответ: 1) $$4\sqrt{3} < 3\sqrt{8}$$, 2) $$4\sqrt{\frac{15}{8}} = \frac{1}{5}\sqrt{750}$$