Which of the following is between π

Question

and 11−−√

Responses

12−−√
Start Root 12 End Root

10−−√
Start Root 10 End Root

8–√
Start Root 8 End Root

7–√

Answer 1

To determine which of the given expressions is between \( \pi \) and \( \sqrt{11} \), we will first find the approximate values of \( \pi \) and \( \sqrt{11} \):

• \( \pi \approx 3.14 \)
• \( \sqrt{11} \approx 3.3166 \)

Now let's compute the approximate values of the other options:

1. \( \sqrt{12} \approx 3.464 \)
2. \( \sqrt{10} \approx 3.162 \)
3. \( \sqrt{8} \approx 2.828 \)
4. \( \sqrt{7} \approx 2.645 \)

Now we can compare these values:

• \( \sqrt{8} \approx 2.828 \): not between \( \pi \) and \( \sqrt{11} \).
• \( \sqrt{7} \approx 2.645 \): not between \( \pi \) and \( \sqrt{11} \).
• \( \sqrt{10} \approx 3.162 \): is between \( \pi \) and \( \sqrt{11} \).
• \( \sqrt{12} \approx 3.464 \): is not between \( \pi \) and \( \sqrt{11} \).

Thus, the only option that is between \( \pi \) and \( \sqrt{11} \) is:

\( \sqrt{10} \).