1. **State the problem:** Simplify the expression $4151 + 3\sqrt{6}$. 2. **Understand the terms:** The expression consists of a whole number $4151$ and a term with a square root $3\sqrt{6}$. These terms are unlike terms and cannot be combined further. 3. **Simplify the square root if possible:** $\sqrt{6}$ cannot be simplified further because 6 is not a perfect square and has no perfect square factors other than 1. 4. **Final expression:** Since the terms are unlike, the expression remains as $4151 + 3\sqrt{6}$. **Answer:** $4151 + 3\sqrt{6}$