What are irrational numbers?
Irrational numbers are real numbers that cannot be expressed as a fraction or ratio of two integers
Irrational numbers are real numbers that cannot be expressed as a fraction or ratio of two integers. In other words, they cannot be written as a terminating or repeating decimal. Irrational numbers have an infinite, non-repeating decimal representation.
Some well-known examples of irrational numbers include:
1. π (pi): The ratio of the circumference of any circle to its diameter. It is approximately equal to 3.14159 and goes on indefinitely without repeating.
2. √2 (square root of 2): It is the length of the diagonal of a square with side length 1. It is an irrational number because it cannot be expressed as a fraction of two integers.
3. √3 (square root of 3): It is the length of the diagonal of an equilateral triangle with side length 1. Like √2, it is also an irrational number.
4. e (Euler’s number): A mathematical constant that is approximately equal to 2.71828. It is commonly used in exponential growth and decay equations.
5. φ (Golden ratio): It is an irrational number that is approximately equal to 1.61803. It appears frequently in geometry and has aesthetic properties that make it visually pleasing.
These are just a few examples, and there are infinitely many other irrational numbers. It is important to note that irrational numbers are an essential part of mathematics and play a crucial role in various mathematical concepts and equations, including algebra, geometry, and calculus.
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