2. Сравните: \(\frac12\sqrt{12}\) и \(\frac13\sqrt{45}\).

\(\frac12\sqrt{12}=\frac12\cdot2\sqrt3=\sqrt3\), а \(\frac13\sqrt{45}=\frac13\cdot3\sqrt5=\sqrt5\).

Так как \(\sqrt3<\sqrt5\), то \(\frac12\sqrt{12}<\frac13\sqrt{45}\).

Ответ: \(\frac12\sqrt{12}<\frac13\sqrt{45}\).