Irrational

How to spell irrational

10 letters · 4 syllables

How to pronounce irrational

Say the part in capitals loudest.

What does irrational mean?

1. adjectiveNot based on clear thought or reason; lacking sound logic.
2. adjectiveOf a number that cannot be written as a ratio of two whole numbers.

Irrational in a sentence

• His irrational fear of lifts forced him to take the stairs to the tenth floor.

• The square root of two is an irrational number whose decimals never repeat.

• The panic buying during the storm was completely irrational.

• Pi is the most famous irrational value in mathematics.

Where does irrational come from?

Language of origin: Latin

This word traces back to the Latin irrationalis, meaning 'without reason', which was built from the negative prefix in- (assimilated to ir- before an r) and rationalis, 'endowed with reason'. At the heart of it sits the Latin noun ratio, which literally meant a reckoning or calculation and, by extension, reasoned thought; the same root gives us 'ratio', 'rational', and even 'reason' itself. English took the word in during the late 1400s, first describing creatures or behaviour lacking the faculty of reason, and later the familiar sense of conduct or fears that defy logic. Mathematicians borrowed it too, calling a number 'irrational' when it cannot be written as a simple ratio of two whole numbers. The spelling trap is the doubled r: the prefix ir- meets the r of ration, so two r's belong there, just as one might expect in 'irregular'.

How the word is built

• ir- (not, a form of in-)
• ration (from Latin ratio: reason, reckoning)
• -al (adjective suffix)