To find the expression equivalent to [tex]\( 8 \sqrt{6} \)[/tex], we need to evaluate the given options and compare their values to [tex]\( 8 \sqrt{6} \)[/tex].
First, let's evaluate the expression [tex]\( 8 \sqrt{6} \)[/tex]:
[tex]\[ 8 \sqrt{6} \approx 19.5959 \][/tex]
Now, let's evaluate the options provided and compare each to [tex]\( 8 \sqrt{6} \)[/tex]:
A. [tex]\(\sqrt{14}\)[/tex]
[tex]\[ \sqrt{14} \approx 3.7417 \][/tex]
B. [tex]\(\sqrt{48}\)[/tex]
[tex]\[ \sqrt{48} \approx 6.9282 \][/tex]
C. [tex]\(\sqrt{96}\)[/tex]
[tex]\[ \sqrt{96} \approx 9.7980 \][/tex]
D. [tex]\(\sqrt{384}\)[/tex]
[tex]\[ \sqrt{384} \approx 19.5959 \][/tex]
Upon comparing these values, we can see that the value of [tex]\( \sqrt{384} \)[/tex] is approximately equal to the value of [tex]\( 8 \sqrt{6} \)[/tex].
Therefore, the expression equivalent to [tex]\( 8 \sqrt{6} \)[/tex] is:
[tex]\[ \boxed{\sqrt{384}} \][/tex]
