Question

show an example of a rational number that is between 10−−√ and 11−−√ .(1 point) Responses 3.1 3.1 103 Start Fraction 10 over 3 end fraction 165 Start Fraction 16 over 5 end fraction 3.4

Answer 1

To find a rational number between \( \sqrt{10} \) and \( \sqrt{11} \), we first need to determine the approximate values of these square roots.

1. **Calculate \( \sqrt{10} \)**:
- \( \sqrt{10} \approx 3.162 \)

2. **Calculate \( \sqrt{11} \)**:
- \( \sqrt{11} \approx 3.317 \)

Now we look for a rational number between these two values. Among the options provided, we can analyze them:

- **3.1**: This is less than 3.162, so it is not between \( \sqrt{10} \) and \( \sqrt{11} \).
- **\( \frac{10}{3} \approx 3.333 \)**: This is greater than \( \sqrt{11} \), so it is not between the two.
- **\( \frac{16}{5} = 3.2 \)**: This is between 3.162 and 3.317.
- **3.4**: This is greater than \( \sqrt{11} \), so it is not between the two.

The only rational number from your list that lies between \( \sqrt{10} \) and \( \sqrt{11} \) is \( \frac{16}{5} \).

Thus, the answer is: **\( \frac{16}{5} \)**.