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!