To estimate the value of \( 6 \times 2 - \sqrt{} \), we first need to clarify the expression, as it seems there might be a missing number under the square root. Assuming you meant \( 6 \times 2 - \sqrt{something} \), let's analyze \( 6 \times 2 \) first:
\[ 6 \times 2 = 12 \]
Now, if we consider \( \sqrt{something} \) needs to be subtracted from 12, we can explore the provided options. If we subtract increasingly larger square roots, we can see where 12 minus some value would result in one of the options.
However, as the problem stands, let's analyze potential common values for \( \sqrt{x} \):
To infer which option is closest to 12 once \( \sqrt{x} \) is subtracted, we need to evaluate:
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If we estimate \( \sqrt{4} = 2 \), then: \[ 12 - 2 = 10 \quad \text{(not an option)} \]
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If \( \sqrt{16} = 4 \), then: \[ 12 - 4 = 8 \quad \text{(closest to 8.4)} \]
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If \( \sqrt{25} = 5 \): \[ 12 - 5 = 7 \quad \text{(this is too low)} \]
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Continuing with \( \sqrt{36} = 6 \): \[ 12 - 6 = 6 \quad \text{(too low)} \]
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Thus, we can see the only relevant reduction of 12 that brings it closest to one of the provided options is: \[ 12 - 4 = 8 \quad \text{(very close to 8.4)} \]
Therefore, among the choices provided, the best estimate based on \( 12 \) minus a reasonable square root value might be the number \( \mathbf{8.4} \).
So the best estimate of \( 6 \times 2 - \sqrt{} \) is: \[ \text{8.4} \]