In that theory an irrational number was the ratio of two incommensurable geometric magnitudes.
The widened idea is that even when a or x is an irrational number we may speak of a or x unit lengths by measure.
A number that cannot be expressed as a ratio between two integers and is not an imaginary number. If written in decimal notation, an irrational number would have an infinite number of digits to the right of the decimal point, without repetition. Pi and the square root of 2 (√2) are irrational numbers.