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

Question

Responses

10−−√
square root of 10 - no response given

8–√
square root of 8 - incorrect

12−−√
square root of 12 - no response given

7–√

Answer 1

To find which of the options is between \( \pi \) and \( \sqrt{11} \), we need to approximate the values of these numbers:

1. \( \pi \) is approximately \( 3.14 \).
2. \( \sqrt{11} \) is approximately \( 3.3166 \).

Now let's evaluate the options:

1. \( \sqrt{10} \): Approximately \( 3.1623 \).
2. \( \sqrt{8} \): Approximately \( 2.8284 \) — too small.
3. \( \sqrt{12} \): Approximately \( 3.4641 \) — too large.
4. \( \sqrt{7} \): Approximately \( 2.6458 \) — too small.

From our calculations:

• \( \sqrt{10} \) (approximately \( 3.1623 \)) is between \( \pi \) and \( \sqrt{11} \) (since \( \pi \approx 3.14 \) and \( \sqrt{11} \approx 3.3166 \)).
• The other options \( \sqrt{8} \), \( \sqrt{12} \), and \( \sqrt{7} \) do not fall within the specified range.

Therefore, the answer is \( \sqrt{10} \).