To determine which of the given options is equivalent to [tex]\( 8 \sqrt{6} \)[/tex], let's evaluate each given option and compare it to [tex]\( 8 \sqrt{6} \)[/tex].
First, calculate [tex]\( 8 \sqrt{6} \)[/tex]:
[tex]\[ 8 \sqrt{6} = 8 \cdot \sqrt{6} = 8 \cdot 2.449489742783178 \approx 19.595917942265423 \][/tex]
We need to check each option:
1. [tex]\( \sqrt{14} \approx 3.7416573867739413 \)[/tex]
2. [tex]\( \sqrt{48} \approx 6.928203230275509 \)[/tex]
3. [tex]\( \sqrt{96} \approx 9.797958971132712 \)[/tex]
4. [tex]\( \sqrt{384} \approx 19.595917942265423 \)[/tex]
Now compare each of these with our target value [tex]\( 19.595917942265423 \)[/tex]:
- [tex]\( \sqrt{14} \approx 3.7416573867739413 \)[/tex], which is not close to 19.595917942265423.
- [tex]\( \sqrt{48} \approx 6.928203230275509 \)[/tex], which is not close to 19.595917942265423.
- [tex]\( \sqrt{96} \approx 9.797958971132712 \)[/tex], which is not close to 19.595917942265423.
- [tex]\( \sqrt{384} \approx 19.595917942265423 \)[/tex], which matches 19.595917942265423 exactly.
Therefore, the correct answer is:
[tex]\[ D. \, \sqrt{384} \][/tex]
