Question

Determine if each number is either rational or irrational
Square root 21
0.45
Nine
15
Square root 25
-5/17
pi

Answer 1

To determine whether each number is rational or irrational, let's review the definitions first:

- **Rational numbers** can be expressed as the quotient of two integers (where the denominator is not zero). Examples include integers, fractions, and terminating or repeating decimals.
- **Irrational numbers** cannot be expressed as a simple fraction; their decimal representations are non-repeating and non-terminating.

Now, let's evaluate each number:

1. **Square root of 21 (√21)**:
- This is an irrational number because it cannot be expressed as a fraction of two integers. Its decimal expansion is non-repeating and non-terminating.

2. **0.45**:
- This is a rational number because it can be expressed as the fraction \( \frac{45}{100} \) or \( \frac{9}{20} \), which is a quotient of two integers.

3. **Nine (9)**:
- This is a rational number because it can be expressed as \( \frac{9}{1} \), which is also a quotient of two integers.

4. **15**:
- This is a rational number because it can be expressed as \( \frac{15}{1} \).

5. **Square root of 25 (√25)**:
- This is a rational number because \( \sqrt{25} = 5 \), which is an integer and can be written as \( \frac{5}{1} \).

6. **-5/17**:
- This is a rational number because it is a fraction of two integers.

7. **Pi (π)**:
- This is an irrational number because it cannot be expressed as a fraction of two integers, and its decimal form is non-repeating and non-terminating.

In summary:
- Square root of 21: **Irrational**
- 0.45: **Rational**
- Nine: **Rational**
- 15: **Rational**
- Square root of 25: **Rational**
- -5/17: **Rational**
- Pi: **Irrational**