To find a rational number that is between \( \sqrt{10} \) and \( \sqrt{11} \), we first need to approximate these square roots.
- \( \sqrt{10} \) is approximately \( 3.162 \).
- \( \sqrt{11} \) is approximately \( 3.317 \).
Now, we need a rational number that lies between these two values. One simple way to find a rational number is to take an average of \( \sqrt{10} \) and \( \sqrt{11} \) but for simplicity, we can also choose a fraction that falls between the two approximate values.
A suitable rational number could be \( \frac{19}{6} \), which is approximately \( 3.167 \) and lies between \( 3.162 \) and \( 3.317 \).
Thus, an example of a rational number between \( \sqrt{10} \) and \( \sqrt{11} \) is:
\[ \frac{19}{6} \]
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