To simplify the square root of negative 81, you need to use the concept of imaginary numbers, because the square root of a negative number is not defined in the real number system.

The square root of $-81$ can be written as:

$\sqrt{-81} = \sqrt{81} \times \sqrt{-1}$

We know that:

$\sqrt{81} = 9 \quad \text{and} \quad \sqrt{-1} = i$

So:

$\sqrt{-81} = 9i$

Thus, the simplified form of the square root of $-81$ is:

$9i$

Would you like more details or further explanations?

Here are 5 related questions:

1. What is the definition of an imaginary number?
2. How do you simplify the square root of a negative number?
3. What is the difference between real and complex numbers?
4. Can the square root of any negative number be simplified?
5. How do you perform operations involving imaginary numbers?

Tip: The imaginary unit $i$ is defined as the square root of $-1$, and it helps represent numbers that are not part of the real number system.