To determine which of the given options falls between \( \pi \) (approximately 3.14) and \( \sqrt{11} \) (approximately 3.3166), we can calculate the approximate values of each option:
- \( \sqrt{8} \) is approximately \( 2.828 \)
- \( \sqrt{7} \) is approximately \( 2.6458 \)
- \( \sqrt{10} \) is approximately \( 3.162 \)
- \( \sqrt{12} \) is approximately \( 3.464 \)
Now, let's compare these values with \( \pi \) and \( \sqrt{11} \):
- \( \pi \approx 3.14 \)
- \( \sqrt{11} \approx 3.3166 \)
Now we can see which value is between \( \pi \) and \( \sqrt{11} \):
- \( \sqrt{8} \approx 2.828 \) (not between)
- \( \sqrt{7} \approx 2.6458 \) (not between)
- \( \sqrt{10} \approx 3.162 \) (this is between)
- \( \sqrt{12} \approx 3.464 \) (not between)
Therefore, the answer is:
\( \sqrt{10} \) (Start Root 10 End Root) is between \( \pi \) and \( \sqrt{11} \).