1. The problem is to simplify the expression $8 \sqrt{6}$. 2. Recall that the square root function $\sqrt{x}$ gives the positive number whose square is $x$. 3. Since $8$ is a coefficient and $\sqrt{6}$ is an irrational number, the expression $8 \sqrt{6}$ is already in its simplest form because $6$ is not a perfect square and cannot be simplified further. 4. Therefore, the simplified form of $8 \sqrt{6}$ is $8 \sqrt{6}$. Final answer: $8 \sqrt{6}$