To simplify \(\frac{3\sqrt{6}}{6}\), follow these steps:

1. **Simplify the fraction**:
   \[
   \frac{3\sqrt{6}}{6} = \frac{3}{6} \times \sqrt{6} = \frac{1}{2} \times \sqrt{6} 
   \]

2. **Write the final answer**:
   \[
   \frac{\sqrt{6}}{2}
   \]

So, the simplified form of \(\frac{3\sqrt{6}}{6}\) is \(\frac{\sqrt{6}}{2}\).

Would you like more details or have any questions?

Here are five related questions to consider:
1. How do you simplify \(\frac{5\sqrt{3}}{10}\)?
2. What is the simplified form of \(\frac{4\sqrt{8}}{16}\)?
3. How do you simplify \(\frac{2\sqrt{12}}{4}\)?
4. What is the value of \(\frac{6\sqrt{2}}{12}\)?
5. How do you simplify \(\frac{7\sqrt{5}}{14}\)?

**Tip**: When simplifying an expression with a square root in the numerator, always check if the coefficients and the square root can be simplified first.

Learn how to simplify \(\frac{3\sqrt{6}}{6}\) with a detailed step-by-step solution. This problem covers square roots and fraction simplification, suitable for high school students.

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