Question

Show an example of a rational number that is between square root 10 and square root 11?

16/5
3.4
10/3
3.1

Answer 1

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

Calculating the square roots, we find:

\[
\sqrt{10} \approx 3.162
\]

\[
\sqrt{11} \approx 3.317
\]

Now we look for a rational number that lies between these two values (approximately between 3.162 and 3.317).

Let's evaluate the given options:

1. **\( \frac{16}{5} = 3.2\)** — This is between 3.162 and 3.317.
2. **\( 3.4\)** — This is greater than \(\sqrt{11}\).
3. **\( \frac{10}{3} \approx 3.333\)** — This is also greater than \(\sqrt{11}\).
4. **\( 3.1\)** — This is less than \(\sqrt{10}\).

From these options, the only rational number that lies between \(\sqrt{10}\) and \(\sqrt{11}\) is:

\(\frac{16}{5} = 3.2\)

Thus, the answer is \( \frac{16}{5} \).