Which of the following is a rational number: √32, √81, √90, or √125? (1 point)
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GPT-4o mini
A rational number is a number that can be expressed as a fraction of two integers (where the denominator is not zero). To determine which of the given square roots is a rational number, we can calculate the square roots:
- \( \sqrt{32} \) is not a perfect square and can be simplified to \( 4\sqrt{2} \), which is irrational.
- \( \sqrt{81} \) is a perfect square, and \( \sqrt{81} = 9 \), which is rational.
- \( \sqrt{90} \) is not a perfect square and can be simplified to \( 3\sqrt{10} \), which is irrational.
- \( \sqrt{125} \) is not a perfect square and can be simplified to \( 5\sqrt{5} \), which is irrational.
Thus, the only rational number among the options is \( \sqrt{81} = 9 \).
So, the answer is **√81**.
- \( \sqrt{32} \) is not a perfect square and can be simplified to \( 4\sqrt{2} \), which is irrational.
- \( \sqrt{81} \) is a perfect square, and \( \sqrt{81} = 9 \), which is rational.
- \( \sqrt{90} \) is not a perfect square and can be simplified to \( 3\sqrt{10} \), which is irrational.
- \( \sqrt{125} \) is not a perfect square and can be simplified to \( 5\sqrt{5} \), which is irrational.
Thus, the only rational number among the options is \( \sqrt{81} = 9 \).
So, the answer is **√81**.
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