Question

Choose the correct description of the number set.

Number set:

(√2 , √5 , 𝛑 )
(-7.4, 0, 3.232323..., √25 )
(-⅚ , ⅞ , π/2 )
(√8 , √9 , √10 )

Description:

Rational numbers only
Irrational number only
Both rational and irrational

Answer 1

Let's analyze each number set to determine if it contains rational or irrational numbers.

1. Set: \( (\sqrt{2}, \sqrt{5}, \pi) \)
- \( \sqrt{2} \) and \( \sqrt{5} \) are irrational numbers.
- \( \pi \) is also an irrational number.
- **Description**: Irrational numbers only

2. Set: \( (-7.4, 0, 3.232323..., \sqrt{25}) \)
- \(-7.4\) is a rational number.
- \(0\) is a rational number.
- \(3.232323...\) (which can be represented as \(3.\overline{23}\)) is a rational number.
- \( \sqrt{25} = 5 \) is a rational number.
- **Description**: Rational numbers only

3. Set: \( (-\frac{5}{6}, \frac{7}{8}, \frac{\pi}{2}) \)
- \(-\frac{5}{6}\) and \(\frac{7}{8}\) are rational numbers.
- \(\frac{\pi}{2}\) is an irrational number (as \(\pi\) is irrational).
- **Description**: Both rational and irrational

4. Set: \( (\sqrt{8}, \sqrt{9}, \sqrt{10}) \)
- \( \sqrt{8} = 2\sqrt{2} \) is irrational.
- \( \sqrt{9} = 3 \) is rational.
- \( \sqrt{10} \) is irrational.
- **Description**: Both rational and irrational

Based on this analysis, here is the summary for each set:

1. \( (\sqrt{2}, \sqrt{5}, \pi) \) - **Irrational numbers only**
2. \( (-7.4, 0, 3.232323..., \sqrt{25}) \) - **Rational numbers only**
3. \( (-\frac{5}{6}, \frac{7}{8}, \frac{\pi}{2}) \) - **Both rational and irrational**
4. \( (\sqrt{8}, \sqrt{9}, \sqrt{10}) \) - **Both rational and irrational**