Question

Which of the following is a rational number: 32−−√
, 81−−√
, 90−−√
, or 125−−−√
?(1 point)

Answer 1

To determine which of the given numbers is a rational number, we need to evaluate the square roots:

1. \( \sqrt{32} \)
2. \( \sqrt{81} \)
3. \( \sqrt{90} \)
4. \( \sqrt{125} \)

A rational number is a number that can be expressed as the quotient of two integers.

- \( \sqrt{32} = \sqrt{16 \cdot 2} = 4\sqrt{2} \), which is irrational.
- \( \sqrt{81} = 9 \), which is rational (it can be expressed as \( \frac{9}{1} \)).
- \( \sqrt{90} = \sqrt{9 \cdot 10} = 3\sqrt{10} \), which is irrational.
- \( \sqrt{125} = \sqrt{25 \cdot 5} = 5\sqrt{5} \), which is irrational.

Therefore, the only rational number among the options is \( \sqrt{81} \).