To solve the given problem, we need to find the quotient of [tex]\(\frac{\sqrt{96}}{\sqrt{8}}\)[/tex].
First, recall that the square root of a quotient can be written as the quotient of the square roots. That is,
[tex]\[
\frac{\sqrt{96}}{\sqrt{8}} = \sqrt{\frac{96}{8}}.
\][/tex]
Next, simplify the fraction inside the square root:
[tex]\[
\frac{96}{8} = 12.
\][/tex]
Then, take the square root of the simplified result:
[tex]\[
\sqrt{12}.
\][/tex]
However, we are interested in confirming if this equals [tex]\(2 \sqrt{3}\)[/tex], so we should break it down:
[tex]\[
\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2 \sqrt{3}.
\][/tex]
Thus, we have:
[tex]\[
\frac{\sqrt{96}}{\sqrt{8}} = 2 \sqrt{3}.
\][/tex]
We can compare this with the provided answer choices:
1. [tex]\(2 \sqrt{3}\)[/tex]
2. 4
3. [tex]\(2 \sqrt{22}\)[/tex]
4. 12
The quotient [tex]\(\frac{\sqrt{96}}{\sqrt{8}} = 2 \sqrt{3}\)[/tex] exactly matches the first choice. Therefore, the correct answer is:
[tex]\[
2 \sqrt{3}
\][/tex]
To confirm numerically, the value of [tex]\(2 \sqrt{3}\)[/tex] is approximately 3.4641. This is indeed what the initial question's result confirms. Thus, the final answer is:
[tex]\[
\boxed{2 \sqrt{3}}
\][/tex]
