To solve the equation [tex]\( x^2 = 121 \)[/tex] using the square root property, follow these steps:
1. Identify the original equation:
[tex]\[
x^2 = 121
\][/tex]
2. Use the square root property:
The square root property states that if [tex]\( x^2 = a \)[/tex], then [tex]\( x = \pm \sqrt{a} \)[/tex].
3. Apply the square root property to the equation:
[tex]\[
x = \pm \sqrt{121}
\][/tex]
4. Simplify the square root:
The square root of [tex]\( 121 \)[/tex] is [tex]\( 11 \)[/tex], because [tex]\( 11 \times 11 = 121 \)[/tex].
5. So the equation becomes:
[tex]\[
x = \pm 11
\][/tex]
6. Express the solution as a set of positive and negative values:
[tex]\[
x = 11, -11
\][/tex]
Therefore, the solutions to the equation [tex]\( x^2 = 121 \)[/tex] are [tex]\( 11 \)[/tex] and [tex]\( -11 \)[/tex].
