Irrational

//ɪˈɹæʃ.(ə.)nəl// adj, noun

adj, noun ·Common ·High school level

Definitions

Noun
  1. 1
    A real number that can not be expressed as the quotient of two integers, an irrational number.

    "The square root of 2, which was the first irrational to be discovered, was known to the early Pythagoreans, and ingenious methods of approximating to its value were discovered."

  2. 2
    a real number that cannot be expressed as a rational number wordnet
Adjective
  1. 1
    Not rational; unfounded, nonsensical or wrong-headed.

    "an irrational decision"

  2. 2
    Of a real number, that cannot be written as the ratio of two integers. not-comparable

    "The number π is irrational."

Adjective
  1. 1
    not consistent with or using reason wordnet
  2. 2
    real but not expressible as the quotient of two integers wordnet

Synonyms

All synonyms
nonrationalreasonlessunreasonableunreasoningabsurdpreposterous

Example

More examples

"The irrational conversation continued."

Etymology

From Latin irratiōnālis, from ir- + ratiōnālis.

Related phrases

irrational numberirrational numberreal number

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Data sourced from Wiktionary, WordNet, CMU, and other open linguistic databases. Updated March 2026.