What is the result of the square root of 2 categorized as?

The square root of 2 is categorized as an irrational number because it cannot be expressed as a fraction of two integers. An irrational number is defined as a number that cannot be written in the form ( \frac{p}{q} ) where ( p ) and ( q ) are integers and ( q \neq 0 ). The decimal representation of the square root of 2 is non-repeating and non-terminating, which further confirms its classification as irrational.

In contrast, rational numbers include integers and whole numbers among other fractions, but since the square root of 2 does not fit these definitions, it stands alone in the irrational category. This property of not being expressible as a simple fraction is what distinguishes the square root of 2 from other number types like integers or whole numbers.