Question

s each number rational or irrational?



Select Rational or Irrational for each number.

Rational Irrational
0.15783456


3^√5


0.23¯¯¯¯


−√200

Answer 1

Let's evaluate each of the given numbers to determine if they are rational or irrational:

1. **0.15783456**: This is a finite decimal, which can be expressed as a fraction (e.g., \( \frac{15783456}{100000000} \)). Therefore, it is **Rational**.

2. **3^√5**: This is an expression involving an irrational number \( \sqrt{5} \). The base 3 is rational, but raising a rational number to an irrational exponent results in an irrational number. Therefore, \( 3^{\sqrt{5}} \) is **Irrational**.

3. **0.23¯¯¯¯**: This notation represents a repeating decimal (0.23232323...). Such numbers can be expressed as a fraction. For example, \( 0.23̅ = \frac{23}{99} \). Therefore, it is **Rational**.

4. **−√200**: The square root of 200 can be simplified to \( -10\sqrt{2} \). Since \( \sqrt{2} \) is irrational, \( -10\sqrt{2} \) is also irrational. Therefore, it is **Irrational**.

In summary:

- **0.15783456**: Rational
- **3^√5**: Irrational
- **0.23¯¯¯¯**: Rational
- **−√200**: Irrational