Let's find the quotient of [tex]\(\frac{\sqrt{96}}{\sqrt{8}}\)[/tex].
First, determine the values of the square roots:
The square root of 96 is approximately 9.797958971132712.
The square root of 8 is approximately 2.8284271247461903.
Next, calculate the quotient by dividing the value of [tex]\(\sqrt{96}\)[/tex] by the value of [tex]\(\sqrt{8}\)[/tex]:
[tex]\[
\frac{9.797958971132712}{2.8284271247461903} \approx 3.464101615137754
\][/tex]
Now, let's compare this quotient with the given choices:
- [tex]\(2 \sqrt{3}\)[/tex]
- 4
- [tex]\(2 \sqrt{22}\)[/tex]
- 12
We need to express 3.464101615137754 in a form that matches one of the given choices.
Knowing that [tex]\(2 \cdot \sqrt{3} \approx 2 \cdot 1.732 \approx 3.464\)[/tex], we can see that the value [tex]\(2 \sqrt{3}\)[/tex] approximately matches the numerical result we calculated.
Therefore, the correct answer is [tex]\(2 \sqrt{3}\)[/tex].
