Question

Which of the following is between π
𝜋
and 11−−√
11
?(1 point)
Responses

8–√
8
Start Root 8 End Root

7–√
7
Start Root 7 End Root

10−−√
10
Start Root 10 End Root

12−−√

Answer 1

To determine which of the given options falls between \( \pi \) and \( \sqrt{11} \), we first need to approximate the values of \( \pi \) and \( \sqrt{11} \):

- \( \pi \approx 3.14 \)
- \( \sqrt{11} \approx 3.32 \) (since \( 3.32^2 = 11 \))

Now, let's approximate the values of the given options:

1. \( \sqrt{8} \approx 2.83 \)
2. \( \sqrt{7} \approx 2.65 \)
3. \( \sqrt{10} \approx 3.16 \) (since \( 3.16^2 \) is a little over 10)
4. \( \sqrt{12} \approx 3.46 \) (since \( 3.46^2 = 12 \))

Now we can compare these approximated values:

- \( \pi \approx 3.14 \)
- \( \sqrt{11} \approx 3.32 \)

Looking at the approximations, we have:

- \( \sqrt{8} \approx 2.83 \) (not between \( \pi \) and \( \sqrt{11} \))
- \( \sqrt{7} \approx 2.65 \) (not between \( \pi \) and \( \sqrt{11} \))
- \( \sqrt{10} \approx 3.16 \) (between \( \pi \) and \( \sqrt{11} \))
- \( \sqrt{12} \approx 3.46 \) (not between \( \pi \) and \( \sqrt{11} \))

Thus, the only value that falls between \( \pi \) and \( \sqrt{11} \) is \( \sqrt{10} \).