### Irrational number

An **irrational number** is a real number that you cannot write as the quotient of two integers.

That is all, they do not defy logic.

##### Explanation

If a number is the quotient of two integers, we call this a rational number. Rational and irrational numbers form together the set of real numbers.

##### Example 1

The square root of 2 is

and is an irrational number.

##### Example 2

The golden ratio is an irrational number

and has the irrational number √5 in the numerator.

## HistoryThe ancient Greek mathematician Hippasus (ca. 530 BC - ca. 450 BC) discovered irrational numbers through geometry. |