Show an example of an irrational number between 9 and 11.

√100

√99

√10

√20

1 answer

To find an irrational number between 9 and 11, let's evaluate each option:

  1. \( \sqrt{100} = 10 \) (This is a rational number).
  2. \( \sqrt{99} \) is approximately 9.95, and it is irrational.
  3. \( \sqrt{10} \) is approximately 3.16, and it is not between 9 and 11.
  4. \( \sqrt{20} \) is approximately 4.47, and it is also not between 9 and 11.

The only number among the options that is both irrational and between 9 and 11 is \( \sqrt{99} \).