To find a rational number that lies between \(\sqrt{10}\) and \(\sqrt{11}\), let's first determine the approximate values of these square roots:
- \(\sqrt{10} \approx 3.162\)
- \(\sqrt{11} \approx 3.317\)
Now, we can choose a rational number that falls between these two values. A simple choice would be \(3.25\) because:
\[ 3.162 < 3.25 < 3.317 \]
Thus, \(3.25\) is a rational number that lies between \(\sqrt{10}\) and \(\sqrt{11}\).
Alternatively, you could also choose \(\frac{13}{4} = 3.25\), which is another way to represent that rational number.
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