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Select the correct answer.

Which expression is equivalent to [tex]$8 \sqrt{6}$[/tex]?

A. [tex]\sqrt{14}[/tex]
B. [tex]\sqrt{48}[/tex]
C. [tex]\sqrt{96}[/tex]
D. [tex]\sqrt{384}[/tex]

Sagot :

GinnyAnsweridn
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]
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