To solve the equation [tex]\( \square^2 = \sqrt{64} \)[/tex], let's follow a step-by-step approach:
1. Calculate [tex]\( \sqrt{64} \)[/tex]:
[tex]\[
\sqrt{64} = 8.0
\][/tex]
So, the equation becomes:
[tex]\[
\square^2 = 8.0
\][/tex]
2. Evaluate the given options to check which one satisfies [tex]\( \square^2 = 8.0 \)[/tex]:
- Option A: [tex]\( \sqrt{8} \)[/tex]
[tex]\[
\sqrt{8} \approx 2.8284271247461903
\][/tex]
Checking if [tex]\((\sqrt{8})^2 = 8.0\)[/tex]:
[tex]\[
(2.8284271247461903)^2 \approx 8.0
\][/tex]
This option satisfies the equation.
- Option B: [tex]\( \sqrt{32} \)[/tex]
[tex]\[
\sqrt{32} \approx 5.656854249492381
\][/tex]
Checking if [tex]\((\sqrt{32})^2 = 8.0\)[/tex]:
[tex]\[
(5.656854249492381)^2 \approx 32.0
\][/tex]
This option does not satisfy the equation.
- Option C: 16
[tex]\[
16
\][/tex]
Checking if [tex]\((16)^2 = 8.0\)[/tex]:
[tex]\[
16^2 = 256.0
\][/tex]
This option does not satisfy the equation.
- Option D: 32
[tex]\[
32
\][/tex]
Checking if [tex]\((32)^2 = 8.0\)[/tex]:
[tex]\[
32^2 = 1024.0
\][/tex]
This option does not satisfy the equation.
3. Conclusion:
Among the options provided, only [tex]\( \sqrt{8} \approx 2.8284271247461903 \)[/tex] satisfies the equation [tex]\( \square^2 = 8.0 \)[/tex].
Hence, the correct option is A. [tex]\( \sqrt{8} \)[/tex].
