1. The problem is to simplify the expression $\sqrt{11} + 4\sqrt{7}$.\n\n2. The expression consists of two terms involving square roots: $\sqrt{11}$ and $4\sqrt{7}$.\n\n3. Important rule: You can only combine like terms with the same radicand (the number inside the square root). Here, $\sqrt{11}$ and $\sqrt{7}$ are different, so they cannot be combined.\n\n4. Therefore, the expression is already in its simplest form: $\sqrt{11} + 4\sqrt{7}$.\n\nFinal answer: $\sqrt{11} + 4\sqrt{7}$