To determine the square roots of 64, we need to identify which numbers, when squared, give us the value 64. Let's evaluate each of the given options:
1. Option A: -8
[tex]\[
(-8) \times (-8) = 64
\][/tex]
Since [tex]\(-8\)[/tex] squared is 64, [tex]\(-8\)[/tex] is a correct answer.
2. Option B: 4
[tex]\[
4 \times 4 = 16
\][/tex]
Since 4 squared is 16, not 64, 4 is not a correct answer.
3. Option C: [tex]\(|8|\)[/tex]
[tex]\[
|8| = 8 \quad \text{and} \quad 8 \times 8 = 64
\][/tex]
Since [tex]\(|8|\)[/tex] simplifies to 8, and 8 squared is 64, [tex]\(|8|\)[/tex] becomes 8 and is a correct answer.
4. Option D: 8
[tex]\[
8 \times 8 = 64
\][/tex]
Since 8 squared is 64, 8 is a correct answer.
5. Option E: 8.5
[tex]\[
8.5 \times 8.5 = 72.25
\][/tex]
Since 8.5 squared is 72.25, not 64, 8.5 is not a correct answer.
6. Option F: -4
[tex]\[
(-4) \times (-4) = 16
\][/tex]
Since [tex]\(-4\)[/tex] squared is 16, not 64, [tex]\(-4\)[/tex] is not a correct answer.
Thus, the correct answers for the square roots of 64 are:
- Option A: -8
- Option C: [tex]\(|8|\)[/tex]
- Option D: 8
