Question

Show an example of a rational number that is between √10 and √11.

options:

16 over 5

3.4

10 over 3

3.1

Answer 1

To find a rational number between \(\sqrt{10}\) and \(\sqrt{11}\), we first need to approximate the values of \(\sqrt{10}\) and \(\sqrt{11}\).

Calculating these square roots:

- \(\sqrt{10} \approx 3.162\)
- \(\sqrt{11} \approx 3.317\)

Now, we are looking for a rational number that lies between approximately 3.162 and 3.317.

Let's evaluate the given options:

1. **\(\frac{16}{5} = 3.2\)** - This number is between 3.162 and 3.317.
2. **\(3.4\)** - This number is greater than 3.317.
3. **\(\frac{10}{3} \approx 3.333\)** - This number is also greater than 3.317.
4. **\(3.1\)** - This number is less than 3.162.

The only option that falls between \(\sqrt{10}\) and \(\sqrt{11}\) is:

\(\frac{16}{5}\) (or 3.2).