Which choice is equivalent to the quotient below?

[tex]\ \textless \ br/\ \textgreater \ \frac{\sqrt{40}}{\sqrt{8}}\ \textless \ br/\ \textgreater \ [/tex]

A. [tex]\sqrt{5}[/tex]

B. [tex]\frac{5}{2}[/tex]

C. 5

D. [tex]\frac{\sqrt{5}}{2}[/tex]



Answer :

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]