Question

What is irrational number

Answer 1

An irrational number is a type of real number that cannot be expressed as a simple fraction, meaning it cannot be written in the form \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \) is not zero. Instead, irrational numbers have non-repeating and non-terminating decimal expansions.

Some common examples of irrational numbers include:

- The square root of any non-perfect square (e.g., \( \sqrt{2} \), \( \sqrt{3} \))
- The mathematical constant \( \pi \) (approximately 3.14159...)
- The mathematical constant \( e \) (approximately 2.71828...)

Irrational numbers are important in mathematics and appear in various contexts, including geometry, calculus, and number theory.