What is the simplest form of \( \frac{2 \sqrt{3}}{\sqrt{6}} \) ?

To simplify \( \frac{2 \sqrt{3}}{\sqrt{6}} \), we can start by rationalizing the denominator. Remember that \( \sqrt{6} = \sqrt{2 \cdot 3} = \sqrt{2} \cdot \sqrt{3} \). Thus, we can rewrite our expression as: \[ \frac{2 \sqrt{3}}{\sqrt{2} \cdot \sqrt{3}} \] Now, we can see that \( \sqrt{3} \) in the numerator and the denominator can be cancelled out. This gives us: \[ \frac{2}{\sqrt{2}} \] Next, we can rationalize the denominator again by multiplying the numerator and denominator by \( \sqrt{2} \): \[ \frac{2 \cdot \sqrt{2}}{\sqrt{2} \cdot \sqrt{2}} = \frac{2\sqrt{2}}{2} = \sqrt{2} \] Thus, the simplest form of \( \frac{2 \sqrt{3}}{\sqrt{6}} \) is \( \sqrt{2} \).