To find a rational number that is between \( \sqrt{10} \) and \( \sqrt{11} \), we first need to approximate the values of these square roots:
- \( \sqrt{10} \) is approximately \( 3.162 \) (more precisely, it's roughly \( 3.162277660168379 \)).
- \( \sqrt{11} \) is approximately \( 3.317 \) (more precisely, it's roughly \( 3.3166247903554 \)).
Next, we look for a rational number between these two values. A simple choice would be the rational number \( \frac{32}{10} \) or \( 3.2 \).
To verify:
- \( 3.162 < 3.2 < 3.317 \)
Thus, \( \frac{32}{10} \) or simply \( 3.2 \) is a rational number between \( \sqrt{10} \) and \( \sqrt{11} \). Other rational numbers could include \( \frac{31}{10} = 3.1 \) or \( \frac{33}{10} = 3.3 \) (3.3 is not acceptable since it exceeds \( \sqrt{11} \)).
In summary, \( \frac{32}{10} \) or simply \( 3.2 \) is a rational number that satisfies the requirement.