To determine which expression is equivalent to [tex]\( 8 \sqrt{6} \)[/tex], we will evaluate each given choice and compare it to [tex]\( 8 \sqrt{6} \)[/tex].
First, consider the given expression [tex]\( 8 \sqrt{6} \)[/tex]:
[tex]\[ 8 \sqrt{6} \approx 19.5959 \][/tex]
Now, let's evaluate each of the given choices:
1. Choice A: [tex]\( \sqrt{14} \)[/tex]
[tex]\[ \sqrt{14} \approx 3.7417 \][/tex]
2. Choice B: [tex]\( \sqrt{48} \)[/tex]
[tex]\[ \sqrt{48} \approx 6.9282 \][/tex]
3. Choice C: [tex]\( \sqrt{90} \)[/tex]
[tex]\[ \sqrt{90} \approx 9.4868 \][/tex]
4. Choice D: [tex]\( \sqrt{386} \)[/tex]
[tex]\[ \sqrt{386} \approx 19.6469 \][/tex]
Comparing these values to [tex]\( 8 \sqrt{6} \approx 19.5959 \)[/tex], we can see that:
- [tex]\(\sqrt{14} \approx 3.7417\)[/tex] is much smaller than [tex]\( 8 \sqrt{6} \)[/tex].
- [tex]\(\sqrt{48} \approx 6.9282\)[/tex] is also smaller than [tex]\( 8 \sqrt{6} \)[/tex].
- [tex]\(\sqrt{90} \approx 9.4868\)[/tex] is still smaller than [tex]\( 8 \sqrt{6} \)[/tex].
- However, [tex]\(\sqrt{386} \approx 19.6469\)[/tex] is very close to [tex]\( 8 \sqrt{6} \)[/tex].
Thus, the expression equivalent to [tex]\( 8 \sqrt{6} \)[/tex] is:
[tex]\[\boxed{\sqrt{386}}.\][/tex]
