Alright, let's solve the given problem step-by-step.
We are given the expression:
[tex]\[ \sqrt{2} \cdot \sqrt{8} \cdot \sqrt{4} \][/tex]
First, let's simplify the square roots involved:
1. Simplifying [tex]\(\sqrt{8}\)[/tex]:
[tex]\[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \][/tex]
2. Simplifying [tex]\(\sqrt{4}\)[/tex]:
[tex]\[ \sqrt{4} = 2 \][/tex]
Now, substituting these simplified forms back into the given expression:
[tex]\[ \sqrt{2} \cdot \sqrt{8} \cdot \sqrt{4} = \sqrt{2} \cdot (2\sqrt{2}) \cdot 2 \][/tex]
Next, let's perform the multiplication step-by-step:
1. Multiply [tex]\(\sqrt{2}\)[/tex] and [tex]\(2\sqrt{2}\)[/tex]:
[tex]\[ \sqrt{2} \cdot 2\sqrt{2} = 2 (\sqrt{2} \cdot \sqrt{2}) = 2 \cdot 2 = 4 \][/tex]
2. Now, multiply the result by 2:
[tex]\[ 4 \cdot 2 = 8 \][/tex]
So, the simplified expression is:
[tex]\[ \sqrt{2} \cdot \sqrt{8} \cdot \sqrt{4} = 8 \][/tex]
Therefore, the correct choice is:
[tex]\[ \boxed{8} \][/tex]
So the answer is choice C.
