How to Identify Irrational Numbers?
The real numbers which cannot be expressed in the form of p/q, where p and q are integers and q ≠ 0 are known as irrational numbers. For example, √2 and √ 3 etc. are irrational. Whereas any number which can be represented in the form of p/q, such that, p and q are integers and q ≠ 0 is known as a rational number.
There are 4 different aspects by which we can conclude the irrational number:
Square Roots of Prime Numbers
If a number is the square root of a non-perfect square (a number that is not the square of an integer), then it is irrational.
Example: √2, √3, and √5 are irrational.
Note: √prime number always gives an irrational number.
Non-Terminating, Non-Repeating Decimals
If the decimal representation of a number goes on forever without repeating, it might be irrational. Rational numbers have decimals that either terminate (like 1/4 = 0.25) or repeat (like 1/3 = 0.333…).
Example: 1/4 = 0.4444…….
Mathematical Constants
Certain mathematical constants, like pi (π) and Euler’s number (e), are known to be irrational.
Note: Pi (π) is an irrational number because it is neither terminating nor repeating decimal.
Rational and Irrational Numbers
Rational numbers and Irrational numbers are real numbers with unlike characteristics. Rational numbers are the numbers which can be represented in the A/B form where B ≠ 0. Irrational numbers are the numbers that cannot be represented in A / B form. In this article, we’ll learn the concepts of rational numbers and irrational numbers and explore the difference between them.
Table of Content
- What is Rational number?
- How to identify rational numbers?
- What are Irrational Numbers?
- How to Identify Irrational Numbers?
- How to Classify Rational and Irrational Numbers?
- Difference Between Rational and Irrational Numbers