Question

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

Answer 1

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**