To determine which of the given options is 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 \( 3.32 \times 3.32 \approx 11 \))
Now we need to calculate the square roots of the options provided:
- \( \sqrt{12} \approx 3.46 \) (since \( 3.46 \times 3.46 \approx 12 \))
- \( \sqrt{10} \approx 3.16 \) (since \( 3.16 \times 3.16 \approx 10 \))
- \( \sqrt{8} \approx 2.83 \) (since \( 2.83 \times 2.83 \approx 8 \))
- \( \sqrt{7} \approx 2.65 \) (since \( 2.65 \times 2.65 \approx 7 \))
Now we compare these values with \( \pi \) and \( \sqrt{11} \):
- \( \sqrt{12} \approx 3.46 \) (greater than \( \sqrt{11} \))
- \( \sqrt{10} \approx 3.16 \) (between \( \pi \) and \( \sqrt{11} \))
- \( \sqrt{8} \approx 2.83 \) (less than \( \pi \))
- \( \sqrt{7} \approx 2.65 \) (less than \( \pi \))
Therefore, the option that is between \( \pi \) and \( \sqrt{11} \) is \( \sqrt{10} \).
1 answer