Question

Show an example of a rational number that is between 10−−√
and 11−−√
.(1 point)
Responses

3.4
3.4

16/5


3.1
3.1

10/3

Answer 1

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

1. The approximate value of \( \sqrt{10} \) is about 3.16.
2. The approximate value of \( \sqrt{11} \) is about 3.32.

Now, we need a rational number that lies within this range (between approximately 3.16 and 3.32).

Let's evaluate the options given:

- **3.4**: This is greater than 3.32, so it is not valid.
- **16/5**: This simplifies to 3.2, which is between 3.16 and 3.32. This is valid.
- **3.1**: This is less than 3.16, so it is not valid.
- **10/3**: This is approximately 3.33, which is greater than 3.32, so it is not valid.

The rational number from the options that is between \( \sqrt{10} \) and \( \sqrt{11} \) is **16/5**.