When you take the square root of both sides of the equation x² = 81, you are looking for the values of x that satisfy this equation. The operation of taking the square root introduces both positive and negative solutions. Therefore, you can express the results as:
x = ±√81
Since the square root of 81 is 9, this simplifies to:
x = ±9
In conclusion, the complete equation that results from taking the square root of both sides is x = 9 or x = -9.