Question

Approximate Values of Irrational Numbers

Answer 1

Irrational numbers are numbers that cannot be expressed as a simple fraction, meaning they cannot be represented as the ratio of two integers. Their decimal representations are non-repeating and non-terminating. Here are some well-known irrational numbers along with their approximate values:

1. **√2** (Square root of 2)
- Approximate value: **1.414**

2. **π** (Pi)
- Approximate value: **3.14159**

3. **e** (Euler's number)
- Approximate value: **2.71828**

4. **√3** (Square root of 3)
- Approximate value: **1.732**

5. **√5** (Square root of 5)
- Approximate value: **2.236**

6. **√7** (Square root of 7)
- Approximate value: **2.646**

7. **√11** (Square root of 11)
- Approximate value: **3.317**

8. **φ** (Golden ratio, approximately 1.618)
- Approximate value: **1.61803**

9. **√6** (Square root of 6)
- Approximate value: **2.449**

10. **√10** (Square root of 10)
- Approximate value: **3.162**

These values are often used in mathematics, science, and engineering, where exact values are not feasible due to their irrational nature but estimates are needed for calculations.