To simplify \( 384 \), we can factor it into its prime factors.
First, we can break it down:
\[ 384 = 3 \times 128 = 3 \times 2^7 \]
Next, let's check if any of the given options match \( 384 \).
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Option 1: \( 6\sqrt{4} \) \[ 6\sqrt{4} = 6 \times 2 = 12 \]
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Option 2: \( 4\sqrt{6} \)
- This term cannot be simplified without knowing its numerical approximation.
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Option 3: \( 86 \)
- Directly, this equals 86.
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Option 4: \( 68 \)
- Directly, this equals 68.
Now, let's evaluate \( 384 \) numerically:
First, let's rearrange \( 384 \) to find \( 4\sqrt{6} \):
\[ 4\sqrt{6} \neq 384 \]
Also, the other options don't directly relate to \( 384 \).
To summarize:
- None of these options simplify to equal \( 384 \).
- On closer inspection, \( 384 \) is not equivalent to either of those simplified options.
Thus, based on the evaluation, none of the answers are correct simplifications of \( 384 \).
Since the problem likely asks for an equivalence, we can clarify the representation of choice \( \sqrt{} \) forms and relook for simplifications to match directly without confusion.
The answer is:
- None of the answers provided (6√4, 4√6, 86, 68) simplify down to \( 384 \).
However, if strictly asked for aligning choices to numerical values previously computed or cross-referenced from the options which factor into \( 384 \), it would stand separate since they're discrete entities.
Can you clarify if the options were effectively misunderstood, or do you wish more exploration directly on \( \sqrt{} \) values through manipulation?