To determine which two values \(2\sqrt{41}\) is between, we first need to calculate \(2\sqrt{41}\).
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Calculate \(\sqrt{41}\): \[ \sqrt{41} \approx 6.4 \text{ (since } 6.4^2 = 40.96 \text{, which is close to 41)} \]
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Multiply by 2: \[ 2\sqrt{41} \approx 2 \times 6.4 = 12.8 \]
Next, we can use a more precise calculation for \(\sqrt{41}\): \[ \sqrt{41} \approx 6.403 \] Then: \[ 2\sqrt{41} \approx 2 \times 6.403 = 12.806 \]
Now we know that \(2\sqrt{41} \approx 12.806\).
Next, we check which values the number \(12.806\) falls between from the options provided:
- Option A: 12.9 and 13
- Option B: 12.7 and 12.8
- Option C: 12.8 and 12.9
- Option D: 13 and 13.1
Since \(12.806\) is greater than \(12.8\) but less than \(12.9\), we confirm that:
\[ 12.8 < 12.806 < 12.9 \]
Thus, the correct answer is:
C. 12.8 and 12.9