Irrational Numbers

An irrational number is a real number that cannot be expressed as a fraction of two integers and does not terminate or repeat. In other words, it cannot be written as a simple fraction.

Properties of Irrational Numbers

• Cannot be expressed as a simple fraction
• Non-terminating and non-repeating decimal expansion
• Existence of irrational numbers can be proved through the method of contradiction
• When added to a rational number, the result is always irrational
• When multiplied by a non-zero rational number, the result is always irrational

Examples of Irrational Numbers

Some common examples of irrational numbers include:

• √2 (square root of 2)
• π (pi)
• e (Euler's number)
• √3 (square root of 3)

Study Tips

When studying irrational numbers, it's important to:

1. Understand the definition and properties of irrational numbers
2. Practice identifying irrational numbers and distinguishing them from rational numbers
3. Learn how to approximate irrational numbers using decimal expansions
4. Use visual aids such as number lines and geometric representations to understand irrational numbers
5. Explore real-world applications of irrational numbers, such as in geometry and trigonometry

Conclusion

Understanding irrational numbers is an important concept in mathematics, and it is essential for various fields including geometry, algebra, and calculus. By grasping the properties and examples of irrational numbers, you can develop a solid foundation for further mathematical studies.

[Irrational Numbers] Related Worksheets and Study Guides:

• Real numbersMathematics • Eighth Grade