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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.



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.



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

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