To determine which of the following is a rational number, we need to check each square root:
-
\( \sqrt{32} \):
- \( 32 = 16 \times 2 \), so \( \sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2} \). Since \( \sqrt{2} \) is irrational, \( \sqrt{32} \) is irrational.
-
\( \sqrt{81} \):
- \( 81 = 9 \times 9 \) or \( 3^4 \), so \( \sqrt{81} = 9 \). This is a rational number.
-
\( \sqrt{90} \):
- \( 90 = 9 \times 10 \), so \( \sqrt{90} = \sqrt{9 \times 10} = 3\sqrt{10} \). Since \( \sqrt{10} \) is irrational, \( \sqrt{90} \) is irrational.
-
\( \sqrt{125} \):
- \( 125 = 25 \times 5 \), so \( \sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5} \). Since \( \sqrt{5} \) is irrational, \( \sqrt{125} \) is irrational.
Therefore, the only rational number among them is \( \sqrt{81} \), which equals 9.