To simplify the given expression [tex]\(\frac{4 \sqrt{6}}{2 \sqrt{2}}\)[/tex], let's work through the steps:
1. Initial Expression:
[tex]\[
\frac{4 \sqrt{6}}{2 \sqrt{2}}
\][/tex]
2. Simplify the Fraction:
First, we can simplify the numerical coefficients (the numbers outside the radicals):
[tex]\[
\frac{4}{2} = 2
\][/tex]
So the expression can be written as:
[tex]\[
2 \cdot \frac{\sqrt{6}}{\sqrt{2}}
\][/tex]
3. Simplify the Radicals:
We now simplify the radicals [tex]\(\frac{\sqrt{6}}{\sqrt{2}}\)[/tex]. Using the property of radicals [tex]\(\frac{\sqrt{a}}{\sqrt{b}} = \sqrt{\frac{a}{b}}\)[/tex], we have:
[tex]\[
\frac{\sqrt{6}}{\sqrt{2}} = \sqrt{\frac{6}{2}} = \sqrt{3}
\][/tex]
4. Combine the Simplifications:
Now we can combine the simplified coefficient and the simplified radical:
[tex]\[
2 \sqrt{3}
\][/tex]
Therefore, the simplified form of the expression [tex]\(\frac{4 \sqrt{6}}{2 \sqrt{2}}\)[/tex] is:
[tex]\[
2 \sqrt{3}
\][/tex]
Answer: The correct answer is [tex]\( \boxed{2 \sqrt{3}} \)[/tex].
