1. **Problem Statement:** Evaluate the square roots in the expressions given: a. $\sqrt{81}$, b. $-\sqrt{81}$, c. $\sqrt{-81}$. 2. **Formula and Rules:** The square root of a positive number $a$ is a number $b$ such that $b^2 = a$. For negative numbers, the square root involves imaginary numbers where $\sqrt{-1} = i$. 3. **Evaluations:** a. $\sqrt{81} = 9$ because $9^2 = 81$. b. $-\sqrt{81} = -9$ because it is the negative of the positive root. c. $\sqrt{-81} = \sqrt{81 \times -1} = \sqrt{81} \times \sqrt{-1} = 9i$ where $i$ is the imaginary unit. 4. **Rules Summary:** - For positive numbers, $\sqrt{a}$ is the positive root. - For negative numbers, $\sqrt{-a} = i\sqrt{a}$ where $a > 0$. - The negative sign outside the root changes the sign of the result. This completes the evaluation and explanation of the square root expressions.