To solve the problem, we need to evaluate the square roots of the perfect squares provided in the expressions. Specifically, we have [tex]\(\sqrt{49}\)[/tex] and [tex]\(\sqrt{64}\)[/tex].
### Step-by-Step Solution:
1. Evaluate [tex]\(\sqrt{49}\)[/tex]:
The number 49 is a perfect square because it can be expressed as [tex]\(7 \times 7\)[/tex]. Therefore:
[tex]\[
\sqrt{49} = 7
\][/tex]
2. Evaluate [tex]\(\sqrt{64}\)[/tex]:
The number 64 is also a perfect square because it can be expressed as [tex]\(8 \times 8\)[/tex]. Therefore:
[tex]\[
\sqrt{64} = 8
\][/tex]
Thus, we have evaluated the square roots of the perfect squares as follows:
[tex]\[
\sqrt{49} = 7 \quad \text{and} \quad \sqrt{64} = 8
\][/tex]
From the provided options:
- [tex]$\pm 9$[/tex] is incorrect because the square root of neither 49 nor 64 is 9.
- [tex]$\pm 4$[/tex] is incorrect because 4 is not the square root of 49 or 64.
- [tex]$\pm 5$[/tex] is incorrect for the same reason as above.
- [tex]$\pm 7$[/tex] correctly identifies the square root of 49.
Hence, the correct response is:
[tex]\[
\sqrt{49} = \pm 7 \quad \text{and} \quad \sqrt{64} = \pm 8
\][/tex]
