To determine the positive and negative square roots of 36, we need to find two numbers that, when squared, yield 36. This can be approached step-by-step:
1. Understand Square Roots:
- The square root of a number [tex]\( x \)[/tex] is a number [tex]\( y \)[/tex] such that [tex]\( y^2 = x \)[/tex].
- For a given positive number, there are always two square roots: one positive and one negative.
2. Identify the Possible Square Roots:
- To find a number whose square is 36, we need to solve the equation:
[tex]\[
y^2 = 36
\][/tex]
- Both [tex]\( y = 6 \)[/tex] and [tex]\( y = -6 \)[/tex] satisfy this equation because:
[tex]\[
6^2 = 36 \quad \text{and} \quad (-6)^2 = 36
\][/tex]
3. Conclusion:
- The positive square root of 36 is 6.
- The negative square root of 36 is -6.
Thus, the positive and negative square roots of 36 are [tex]\( \pm 6 \)[/tex].
The correct answer is C. [tex]\( \pm 6 \)[/tex].
