Question

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

3.4

3.1

16/5

10/3

Answer 1

what is the answer

Answer 2

To find a rational number between \( \sqrt{10} \) and \( \sqrt{11} \), we can first approximate the square roots:

\[
\sqrt{10} \approx 3.16
\]
\[
\sqrt{11} \approx 3.32
\]

Thus, we're looking for a rational number between approximately 3.16 and 3.32.

Now, let's evaluate the given options:

- **3.4**: This is greater than 3.32, so it is not between \( \sqrt{10} \) and \( \sqrt{11} \).

- **3.1**: This is less than 3.16, so it is not between \( \sqrt{10} \) and \( \sqrt{11} \).

- **16/5**: This equals \( 3.2 \), which is between 3.16 and 3.32.

- **10/3**: This equals approximately \( 3.33 \), which is greater than \( \sqrt{11} \).

From the possibilities given, **16/5** (which is equal to 3.2) is the only rational number that lies between \( \sqrt{10} \) and \( \sqrt{11} \).

Answer 3

The answer is **16/5**. This rational number (which equals 3.2) is between \( \sqrt{10} \) and \( \sqrt{11} \).