Irrational Numbers

An irrational number is a real number that cannot be expressed as a simple fraction. In other words, it cannot be written in the form a/b, where a and b are integers and b is not equal to 0. The decimal representation of an irrational number goes on forever without repeating.

Examples of Irrational Numbers

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

Properties of Irrational Numbers

• They cannot be expressed as a simple fraction
• The decimal representation goes on forever without repeating

Study Guide

To understand irrational numbers, it's important to remember the following:

1. Review the concept of real numbers and how they are classified.
2. Understand the difference between rational and irrational numbers.
3. Practice identifying irrational numbers and their properties.
4. Learn how to approximate irrational numbers using decimal expansions.
5. Explore the relationship between irrational numbers and geometric concepts, such as the diagonal of a square being an irrational number.

By mastering the concept of irrational numbers, you'll have a solid foundation for more advanced mathematical topics, such as real analysis and number theory.