Final answer:
The equation (y+90)^2 - 81 = 0 can be solved by taking the square root of both sides and then subtracting 90, which results in two solutions, y = -81 and y = -99.
Step-by-step explanation:
To solve the equation (y+90)^2 - 81 = 0 using the square root property, you first isolate the perfect square on one side of the equation:
(y+90)^2 = 81
Next, take the square root of both sides of the equation to get rid of the square on the left side:
√(y+90)^2 = ±√81
This simplifies to:
y + 90 = ± 9
To find the value of y, subtract 90 from both sides of the equation, and consider both the positive and the negative square root of 81:
- y + 90 - 90 = 9 - 90, which simplifies to y = -81
- y + 90 - 90 = -9 - 90, which simplifies to y = -99
Therefore, the solution to the equation are y = -81 and y = -99.