Determine which two values the following expression is between.

2√41

A.
12.9 and 13
B.
12.7 and 12.8
C.
12.8 and 12.9
D.
13 and 13.1

1 answer

To determine which two values \(2\sqrt{41}\) is between, we first need to calculate \(2\sqrt{41}\).

  1. Calculate \(\sqrt{41}\): \[ \sqrt{41} \approx 6.4 \text{ (since } 6.4^2 = 40.96 \text{, which is close to 41)} \]

  2. 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