To find an irrational number between 9 and 11, we can use the square root of a number that is not a perfect square.
From the options given:
- \( \sqrt{99} \) is between 9 and 11 because \( 9^2 = 81 \) and \( 10^2 = 100 \).
- \( \sqrt{100} = 10 \), which is not an irrational number.
- \( \sqrt{20} \) is approximately 4.47, which is not between 9 and 11.
- \( \sqrt{10} \) is approximately 3.16, which is also not between 9 and 11.
Therefore, among the given options, the correct choice showing an irrational number between 9 and 11 is:
\( \sqrt{99} \)