1. **State the problem:** We need to simplify the expression $3\sqrt{6} + 9$. 2. **Recall the components:** The term $3\sqrt{6}$ is a product of 3 and the square root of 6, which is an irrational number. The term 9 is a rational number. 3. **Simplify the expression:** Since $3\sqrt{6}$ and 9 are unlike terms (one is irrational, the other rational), they cannot be combined further. 4. **Final answer:** The expression remains as $3\sqrt{6} + 9$. This is the simplest form because the square root of 6 cannot be simplified further and it cannot be combined with the integer 9.