# Irrational numbers definition explained with example

Do you know what are the irrational numbers and how to give the irrational numbers definition? Irrational numbers are one of the types of numbers that we have in mathematics.

By the name irrational, we get some idea that it is not a rational number. Actually, after learning rational numbers we are going to study about irrational numbers. So if you know rational numbers definition then writing irrational numbers definition is not that much difficult. Now let’s start learning about irrational numbers.

## Irrational numbers definition and example:

Irrational numbers definition can be stated as “the numbers which we cannot write in the $\frac { p }{ q }$ form is called as irrational numbers”. Another definition we can give as “non terminating non recurring decimal numbers are irrational numbers”. The meaning of non terminating Is division process does not end i.e. remainder won’t become zero and recurring means some set of digits will be repeating continuously.

Examples:

$\sqrt { 23 }$ , $\sqrt { 91 }$ ,$\sqrt { 147 }$  ,$\sqrt { 253 }$ , ………………

1.232621247536510245237890123698017845211…………..

0.1014578129658702384308705957198124587………………

Some Example problems on irrational numbers:

Is $\sqrt { 27 }$ is an irrational number? If yes give the reason.

Solution:

Yes, it is an irrational number because it satisfies irrational numbers definition.

Check Whether $\sqrt { 49 }$ is irrational or not?

Solution:

$\sqrt { 49 }$ Is not an irrational number because its value is equals to 7 which is a rational number.

Note:

Under root, if there is a perfect square number then it is not an irrational number.

Example:

$\sqrt { 81 }$,$\sqrt { 64 }$ ,$\sqrt { 4 }$,  …………are not irrational numbers because under root all are perfect square numbers.

Suppose under root if there is a non perfect square number then it is an irrational number.

Example:

$\sqrt { 7 }$ ,$\sqrt { 55 }$ ,$\sqrt { 61 }$ , ………………are irrational numbers because under root all are non perfect square numbers.

Hope that irrational numbers definition is clear and I hope you understood it.