Show an example of a rational number that is between 10−−√

Question

and 11−−√
.(1 point)
Responses

3.4
3.4

16/5
Start Fraction 16 over 5 end fraction

10/3
Start Fraction 10 over 3 end fraction

3.1

Answer 1

To find a rational number that is between \(\sqrt{10}\) and \(\sqrt{11}\), first, we need to determine the approximate decimal values of these square roots:

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

Now, we can look at the provided options:

1. 3.4 is greater than \(\sqrt{11}\) (3.4 > 3.317), so it is not between the two square roots.
2. \(\frac{16}{5}\) (which is 3.2) is between \(\sqrt{10}\) and \(\sqrt{11}\) (3.162 < 3.2 < 3.317).
3. \(\frac{10}{3}\) (approximately 3.333) is greater than \(\sqrt{11}\) (3.333 > 3.317), so it is not between the two square roots.
4. 3.1 is less than \(\sqrt{10}\) (3.1 < 3.162), so it is not between the two square roots.

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

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