To approximate \(\sqrt{11}\), we start by determining its approximate value.
Calculating the squares of whole numbers around 11:
- \(3^2 = 9\)
- \(4^2 = 16\)
Since \(9 < 11 < 16\), we know that \(3 < \sqrt{11} < 4\).
To get a more precise approximation, we can check some numbers between 3 and 4.
Calculating \((3.3)^2\): \[ 3.3^2 = 10.89 \] Calculating \((3.4)^2\): \[ 3.4^2 = 11.56 \] Since \(10.89 < 11 < 11.56\), we narrow it down to \(3.3 < \sqrt{11} < 3.4\).
An even closer approximation might be \(3.32\) or \(3.31\) and checking these: \[ 3.31^2 \approx 10.9561 \quad (too low) \] \[ 3.32^2 \approx 11.0224 \quad (too high) \]
So, it’s safe to conclude that \(\sqrt{11} \approx 3.32\).
Now referring back to the points on your number line:
- Point A is located at 1
- Point B is located at 3
- Point C is located at 4
- Point D is located at 5
Given that \(\sqrt{11} \approx 3.32\), the point that approximates \(\sqrt{11}\) is closest to point B at 3.
Thus, the best answer is:
B