[tex]$
\sqrt{49}\ \textless \ \sqrt{56}\ \textless \ \sqrt{64}
$[/tex]

Evaluate the square roots of the perfect squares.

[tex]$
\sqrt{49} = \quad \sqrt{64} =
$[/tex]

A. [tex]$\pm 9$[/tex]

B. [tex]$\pm 4$[/tex]

C. [tex]$\pm 5$[/tex]

D. [tex]$\pm 7$[/tex]



Answer :

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]