Answer:
To solve the equation (x+5)^(2) = 81 using the square root property, we can follow these steps:
1. Rewrite the equation in square root form: (x+5)^(2) = 81 can be rewritten as √((x+5)^(2)) = √81.
2. Take the square root of both sides of the equation: √((x+5)^(2)) = √81 becomes |x+5| = 9.
3. Split the equation into two separate equations: Since the square root of a number is always positive, we can have two cases:
Case 1: x+5 = 9
Solve for x: x = 9 - 5 = 4
Case 2: x+5 = -9
Solve for x: x = -9 - 5 = -14
So, the solutions to the equation (x+5)^(2) = 81 are x = 4 and x = -14.