2) \( \frac{\sqrt{3}}{\sqrt{6}} \)

To simplify \( \frac{\sqrt{3}}{\sqrt{6}} \), you can multiply the numerator and the denominator by \( \sqrt{6} \) to rationalize it. This gives you \( \frac{\sqrt{3} \cdot \sqrt{6}}{6} = \frac{\sqrt{18}}{6} \). Since \( \sqrt{18} = 3\sqrt{2} \), you can break it down further to arrive at \( \frac{3\sqrt{2}}{6} = \frac{\sqrt{2}}{2} \). Voilà! Now you have a much neater expression, \( \frac{\sqrt{2}}{2} \), which pops up in various areas of math, especially in trigonometry when dealing with angles in a unit circle, making it a handy tool in your math toolkit!