To solve the problem, we need to find the value of the quotient [tex]\(\frac{\sqrt{40}}{\sqrt{8}}\)[/tex].
First, let's calculate [tex]\(\sqrt{40}\)[/tex]. The value of [tex]\(\sqrt{40}\)[/tex] is approximately 6.324555320336759.
Next, let's calculate [tex]\(\sqrt{8}\)[/tex]. The value of [tex]\(\sqrt{8}\)[/tex] is approximately 2.8284271247461903.
We then divide [tex]\(\sqrt{40}\)[/tex] by [tex]\(\sqrt{8}\)[/tex]:
[tex]\[
\frac{\sqrt{40}}{\sqrt{8}} \approx \frac{6.324555320336759}{2.8284271247461903}
\][/tex]
Performing the division gives us approximately 2.23606797749979.
Now, let's find which of the given choices is equivalent to this result:
A. [tex]\(\sqrt{5} \approx 2.23606797749979\)[/tex]
B. [tex]\(\frac{5}{2} = 2.5\)[/tex]
C. 5
D. [tex]\(\frac{\sqrt{5}}{2} \approx 1.118033988749895\)[/tex]
We notice that the value of choice A, [tex]\(\sqrt{5}\)[/tex], is approximately 2.23606797749979, which matches the quotient we computed.
Therefore, the correct choice is:
[tex]\[
\boxed{\sqrt{5}}
\][/tex]
