Question

Approximate Values of Irrational Numbers Practice

Answer 1

Sure! Here are some common irrational numbers along with their approximate values, and we can also practice estimating them together.

### Common Irrational Numbers

1. **π (Pi)**
- Approximate Value: 3.14 or 22/7

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

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

4. **√5 (Square root of 5)**
- Approximate Value: 2.236

5. **e (Euler's Number)**
- Approximate Value: 2.718

6. **Golden Ratio (φ)**
- Approximate Value: 1.618

### Practice Questions

1. **Estimate the value of √8.**
- Since √8 = √(4*2) = √4 * √2 = 2 * 1.414 ≈ 2.828.

2. **Estimate the value of √10.**
- √10 falls between √9 (which is 3) and √16 (which is 4). A rough estimate would be around 3.16 since 10 is closer to 9.

3. **Estimate the value of π + √5.**
- Using the approximate values:
- π ≈ 3.14
- √5 ≈ 2.236
- So, π + √5 ≈ 3.14 + 2.236 ≈ 5.376.

4. **Estimate the value of e^2.**
- Using e ≈ 2.718, e^2 ≈ 2.718 * 2.718 ≈ 7.39.

5. **Add √2 and √3.**
- √2 ≈ 1.414 and √3 ≈ 1.732,
- So, √2 + √3 ≈ 1.414 + 1.732 ≈ 3.146.

### Additional Practice Problems

- Estimate the value of √12.
- Calculate π × √2.
- Find the approximate value of e + φ.

Feel free to work through these and let me know what estimates you come up with!