Question

Is each number rational or irrational?



Select Rational or Irrational for each number.

Rational Irrational
0.5


24−−√


3.42859873


64−−√3

Answer 1

Let's evaluate each of the numbers:

1. **0.5**: This is a decimal representation of the fraction \( \frac{1}{2} \), which is a rational number.
- **Answer: Rational**

2. **\( \sqrt{24} \)**: This can be simplified to \( \sqrt{4 \cdot 6} = 2\sqrt{6} \). Since \( \sqrt{6} \) is an irrational number, \( 2\sqrt{6} \) is also irrational.
- **Answer: Irrational**

3. **3.42859873**: This is a finite decimal, which can be expressed as a fraction. Therefore, it is a rational number.
- **Answer: Rational**

4. **\( 64\sqrt{3} \)**: The number \( \sqrt{3} \) is irrational, and multiplying it by 64 (a rational number) keeps it irrational.
- **Answer: Irrational**

So the classifications are:
- 0.5: Rational
- \( \sqrt{24} \): Irrational
- 3.42859873: Rational
- \( 64\sqrt{3} \): Irrational