Question

Show an example of a rational number that is between the square root of10 and the square root of11. (1 point)

• 3.1
• 10/3
• 3.4
• 16/5

Answer 1

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:

1. **3.1**: This is less than 3.162.
2. **10/3**: This is approximately \(3.333\), which is greater than 3.317.
3. **3.4**: This is also greater than 3.317.
4. **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**.