Question

Select the correct description for each number set.(4 points)
a) (25−−√, 9, −−−√64−−√
)

b) ( -2.4, 0, 3.1, 81−−√
)

c) (−23, 79, π2
)

d) (12−−√, 11−−√, π
)

Answer 1

Let's analyze each number set by identifying the types of numbers contained within them.

### a) (25−−√, 9, −−−√64−−√)
- **Elements**:
- \( \sqrt{25} = 5 \) (rational number)
- \( 9 \) (rational number)
- \( \sqrt{64} = 8 \) (rational number)
- **Description**: All members of this set are rational numbers.
- **Type**: **Rational Numbers**

### b) (-2.4, 0, 3.1, 81−−√)
- **Elements**:
- \(-2.4\) (rational number)
- \(0\) (rational number)
- \(3.1\) (rational number)
- \( \sqrt{81} = 9 \) (rational number)
- **Description**: All members of this set are rational numbers.
- **Type**: **Rational Numbers**

### c) (−23, 79, π2)
- **Elements**:
- \(-23\) (integer, hence rational)
- \(79\) (integer, hence rational)
- \( \pi^2 \) (irrational number; the square of π is not a rational number)
- **Description**: This set contains both rational (the integers) and irrational (the \( \pi^2 \)).
- **Type**: **Mixed (Rational and Irrational)**

### d) (12−−√, 11−−√, π)
- **Elements**:
- \( \sqrt{12} \) (irrational number)
- \( \sqrt{11} \) (irrational number)
- \( \pi \) (irrational number)
- **Description**: All members of this set are irrational numbers.
- **Type**: **Irrational Numbers**

### Final Answer:
a) Rational Numbers
b) Rational Numbers
c) Mixed (Rational and Irrational)
d) Irrational Numbers