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

1 answer

To find a rational number between √10 and √11, we can start by finding the decimal approximation for both square roots.

√10 ≈ 3.162
√11 ≈ 3.317

We can then take the average of these two decimal approximations to find a rational number between them:

(3.162 + 3.317)/2 ≈ 3.24

Therefore, a rational number between √10 and √11 is approximately 3.24.