To find a rational number 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 need to find a rational number between 3.162 and 3.317.
Let's evaluate the options:
- 3.1: This is less than 3.162.
- 10/3: This is approximately \(3.333\), which is greater than 3.317.
- 3.4: This is also greater than 3.317.
- 16/5: This is \(3.2\), which is between 3.162 and 3.317.
The only rational number from the given options that lies between \(\sqrt{10}\) and \(\sqrt{11}\) is:
16/5.