Question

Show an example of a rational number that is between 10−−√ and 11−−√ .(1 point)Responses3.13.1165Start Fraction 16 over 5 end fraction103Start Fraction 10 over 3 end fraction3.43.4

Answer 1

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

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

Now, we can look for rational numbers between these two values.

From the choices provided:

1. \(3.1\)
2. \(3.1165\)
3. \(\frac{16}{5} = 3.2\)
4. \(10\)
5. \(\frac{10}{3} \approx 3.333\)
6. \(3.4\)

The numbers that fall between \(3.162\) and \(3.317\) are \(3.2\) and \(3.1165\).

So, both \(3.1165\) and \(\frac{16}{5}\) (which equals \(3.2\)) are rational numbers between \(\sqrt{10}\) and \(\sqrt{11}\).

If you are asked to select just one, then \(3.2\) (or \(\frac{16}{5}\)) is a clear choice, as it is a simple rational representation.