To determine which given expression is equivalent to [tex]\(8 \sqrt{6}\)[/tex], let's break down each of the options and compare them.
First, let's evaluate the given expression [tex]\(8 \sqrt{6}\)[/tex]:
[tex]\[ 8 \sqrt{6} \][/tex]
Now let's evaluate each option to see if they match [tex]\(8 \sqrt{6}\)[/tex]:
Option A: [tex]\(\sqrt{384}\)[/tex]
[tex]\[ \sqrt{384} \][/tex]
Option B: [tex]\(\sqrt{96}\)[/tex]
[tex]\[ \sqrt{96} \][/tex]
Option C: [tex]\(\sqrt{48}\)[/tex]
[tex]\[ \sqrt{48} \][/tex]
Option D: [tex]\(\sqrt{576}\)[/tex]
[tex]\[ \sqrt{576} \][/tex]
By comparing these options with [tex]\(8 \sqrt{6}\)[/tex], we find that:
[tex]\[ 8 \sqrt{6} = \sqrt{384} \][/tex]
Thus, the expression [tex]\(8 \sqrt{6}\)[/tex] is equivalent to [tex]\(\sqrt{384}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{A} \][/tex]
