1. The problem is to simplify $3\sqrt{-81}$.\n\n2. Recall that the square root of a negative number involves the imaginary unit $i$, where $i=\sqrt{-1}$.\n\n3. We can rewrite $\sqrt{-81}$ as $\sqrt{81 \times -1} = \sqrt{81} \times \sqrt{-1} = 9i$.\n\n4. Now multiply by 3: $3 \times 9i = 27i$.\n\n5. Therefore, the simplified form of $3\sqrt{-81}$ is $27i$.