Among the numbers listed:
- \( \sqrt{32} \) is not a rational number because it can be expressed as \( 4\sqrt{2} \), and \( \sqrt{2} \) is irrational.
- \( \sqrt{81} = 9 \), which is a rational number.
- \( \sqrt{90} \) is not a rational number as it can be simplified to \( 3\sqrt{10} \), and \( \sqrt{10} \) is irrational.
- \( \sqrt{125} = 5\sqrt{5} \), which is also not a rational number since \( \sqrt{5} \) is irrational.
Thus, the only rational number among the given options is \( \sqrt{81} \), which equals 9.