To solve the equation $x^2 = 121$ and find the root(s):

1. Start with the given equation: $x^2 = 121$

2. To isolate $x$, take the square root of both sides. Remember, taking the square root yields both positive and negative roots: $x = \pm \sqrt{121}$

3. Calculate the square root of 121: $x = \pm 11$

Thus, the solutions are $x = 11$ and $x = -11$.

The correct answer is D. $x = \pm 11$.

Would you like more details or have any questions?

Here are five related questions to deepen understanding:

1. What would be the roots if the equation were $x^2 = 144$?
2. How would the answer change if the equation were $x^2 = -121$?
3. Why do we consider both positive and negative roots when taking square roots?
4. Can you solve for $x$ in the equation $x^2 = 64$?
5. What is the significance of taking the absolute value of a square root in some cases?

Tip: Remember, when solving $x^2 = a$ (where $a$ is positive), the solution will always be $x = \pm \sqrt{a}$.