To solve the equation $(x - 7)^2 = 81$ using the square root property, follow these steps:

Step 1: Apply the square root property

The square root property states that if $a^2 = b$, then $a = \pm\sqrt{b}$.

Apply this property to the equation: $(x - 7)^2 = 81$ $x - 7 = \pm\sqrt{81}$

Step 2: Simplify the square root

Calculate the square root of 81: $x - 7 = \pm 9$

Step 3: Solve for $x$

Now, solve for $x$ by adding 7 to both sides for each case:

Case 1: $x - 7 = 9$ $x = 9 + 7$ $x = 16$

Case 2: $x - 7 = -9$ $x = -9 + 7$ $x = -2$

Final Answer

The solutions to the equation $(x - 7)^2 = 81$ are: $x = 16 \quad \text{or} \quad x = -2$

Would you like further details on any step, or do you have any questions?

Here are five related questions for further exploration:

1. How would the solution change if the equation were $(x + 7)^2 = 81$?
2. Can you solve the equation $(2x - 3)^2 = 49$ using the square root property?
3. What happens if the right-hand side of the equation is a negative number?
4. How can the square root property be applied to equations with complex solutions?
5. Can you solve the equation $x^2 - 4x + 4 = 25$ using the square root property?

Tip: When using the square root property, always consider both the positive and negative square roots to ensure you find all possible solutions.