Let's solve the problem step-by-step:
1. Calculate the square roots:
- The square root of [tex]\( 64 \)[/tex] is [tex]\( \sqrt{64} = 8.0 \)[/tex].
- The square root of [tex]\( 4 \)[/tex] is [tex]\( \sqrt{4} = 2.0 \)[/tex].
2. Compute the quotient:
[tex]\[
\frac{\sqrt{64}}{\sqrt{4}} = \frac{8.0}{2.0} = 4.0
\][/tex]
3. Compare the quotient to the given choices:
- Choice A. [tex]\( 4 \)[/tex]: The quotient [tex]\( 4.0 \)[/tex] is exactly 4, so this is equivalent.
- Choice B. [tex]\( \frac{\sqrt{4}}{4} \)[/tex]: Let's evaluate this:
[tex]\[
\frac{\sqrt{4}}{4} = \frac{2.0}{4} = 0.5
\][/tex]
This is not equivalent to [tex]\( 4.0 \)[/tex].
- Choice C. [tex]\( \frac{\sqrt{8}}{2} \)[/tex]: Let's evaluate this:
[tex]\[
\frac{\sqrt{8}}{2} = \frac{2.828}{2} \approx 1.414
\][/tex]
This is not equivalent to [tex]\( 4.0 \)[/tex].
- Choice D. [tex]\( \sqrt{2} \)[/tex]: The square root of 2 is approximately:
[tex]\[
\sqrt{2} \approx 1.414
\][/tex]
This is not equivalent to [tex]\( 4.0 \)[/tex].
After evaluating all the choices, we find that Choice A, which is [tex]\( 4 \)[/tex], is the correct answer. Thus, the equivalent choice is:
[tex]\[
\boxed{4}
\][/tex]
