To solve the equation \( x^2 = 121 \), we can take the square root of both sides. The solutions are:
\[ x = \sqrt{121} \quad \text{or} \quad x = -\sqrt{121} \]
Calculating the square root:
\[ \sqrt{121} = 11 \]
Thus, the solutions are:
\[ x = 11 \quad \text{and} \quad x = -11 \]
Now looking at your responses:
- \( \sqrt{121} \) (which equals 11) is a solution.
- \( \sqrt{-121} \) is not a real solution, since it involves the square root of a negative number.
- \( 11 \) is a solution.
- \( 12 \) is not a solution.
- \( -12 \) is not a solution.
- \( -11 \) is a solution.
So, the solutions to the equation \( x^2 = 121 \) from your options are:
- \( \sqrt{121} \) (11)
- \( 11 \)
- \( -11 \)
Therefore, the valid responses are \( \sqrt{121} \), \( 11 \), and \( -11 \).