Сравните $$6\frac{1}{6}$$ и $$\frac{1}{3}\sqrt{45}$$.

$$6\frac{1}{6} = \frac{37}{6}$$ $$\frac{1}{3}\sqrt{45} = \frac{1}{3}\sqrt{9 \cdot 5} = \frac{1}{3} \cdot 3 \sqrt{5} = \sqrt{5}$$ Сравним $$\frac{37}{6}$$ и $$\sqrt{5}$$: $$\frac{37}{6} \approx 6,17$$ $$\sqrt{5} \approx 2,24$$ $$\frac{37}{6} > \sqrt{5}$$ $$\textbf{Ответ: } 6\frac{1}{6} > \frac{1}{3}\sqrt{45}$$