To solve the equation $x^2 - 121 = 0$ using square roots, follow these steps:

Step 1: Isolate $x^2$ on one side of the equation

$x^2 - 121 = 0$ Add $121$ to both sides: $x^2 = 121$

Step 2: Take the square root of both sides

$x = \pm \sqrt{121}$

Step 3: Simplify the square root

$x = \pm 11$

Final Answer:

$x = 11 \quad \text{or} \quad x = -11$

Do you want further explanation or have additional questions?

Here are 5 related questions to explore further:

1. What is the method for solving quadratic equations other than square roots?
2. How do you solve $x^2 - c = 0$ for other values of $c$?
3. Can all quadratic equations be solved using the square root method?
4. How does the square root method differ from completing the square?
5. How do we handle equations like $(x - a)^2 - c = 0$?

Tip: Always verify your solutions by substituting them back into the original equation to check for correctness.