Question

Select the correct description for each number set. Rational, Irrational, or both?
(25−−√, 9, −−−√64−−√)

( -2.4, 0, 3.1, 81−−√)

(−23, 79, π2)

(12−−√, 11−−√, π)

Answer 1

Let's analyze each set of numbers to determine whether each number is rational, irrational, or both:

1. **Set: \( (\sqrt{25}, 9, \sqrt{64}) \)**
- \(\sqrt{25} = 5\) (rational)
- \(9\) (rational)
- \(\sqrt{64} = 8\) (rational)
**Description: Rational**

2. **Set: \( (-2.4, 0, 3.1, \sqrt{81}) \)**
- \(-2.4\) (rational)
- \(0\) (rational)
- \(3.1\) (rational)
- \(\sqrt{81} = 9\) (rational)
**Description: Rational**

3. **Set: \( (-23, 79, \pi^2) \)**
- \(-23\) (rational)
- \(79\) (rational)
- \(\pi^2\) (irrational, because \(\pi\) is irrational and the square of an irrational number is also irrational)
**Description: Both (since there are both rational and irrational numbers in the set)**

4. **Set: \( (\sqrt{12}, \sqrt{11}, \pi) \)**
- \(\sqrt{12}\) (irrational, can be simplified to \(2\sqrt{3}\))
- \(\sqrt{11}\) (irrational)
- \(\pi\) (irrational)
**Description: Irrational**

### Summary of Descriptions:
1. Rational
2. Rational
3. Both
4. Irrational