To solve the equation [tex]\( x^2 = 36 \)[/tex] using the square root property, follow these steps:
1. Understand the equation: The equation given is [tex]\( x^2 = 36 \)[/tex]. This means that some number [tex]\( x \)[/tex] squared equals 36.
2. Apply the square root property: To find the value of [tex]\( x \)[/tex], you can take the square root of both sides of the equation. The square root property states that if [tex]\( x^2 = k \)[/tex], then [tex]\( x = \pm \sqrt{k} \)[/tex]. Here, [tex]\( k = 36 \)[/tex].
3. Calculate the square root of 36:
[tex]\[
\sqrt{36} = 6.
\][/tex]
4. Consider both positive and negative roots: Since squaring either a positive or a negative number will result in a positive product, we must include both the positive and negative solutions. Thus:
[tex]\[
x = \pm 6.
\][/tex]
This gives us the two solutions:
[tex]\[
x = 6 \quad \text{or} \quad x = -6.
\][/tex]
Hence, the simplified solutions to the equation [tex]\( x^2 = 36 \)[/tex] are:
[tex]\[
x = 6 \quad \text{and} \quad x = -6.
\][/tex]
