English Reference
adjective · noun

irrational

adj. · n.
US /ˌɪˈɹæʃənəɫ/ UK /ɪɹˈæʃənəl/ ir·ra·tional UK spelling irrationals

  1. 01 B2 Upper Intermediate

    adj.not based on reason or clear thinking.

    adj.lacking logical justification or sound reasoning; often used to describe emotions, fears, or decisions.

    Simple

    She had an irrational fear of spiders, even though she knew they were harmless.

    In context

    The market's reaction was entirely irrational, driven more by panic and hearsay than by any concrete changes in economic data.

  2. 02 C1 Advanced Technical Math

    adj.describes a number that cannot be written as a simple fraction.

    adj.relating to a real number that cannot be expressed as a ratio of two integers.

    Simple

    Pi is the most famous example of an irrational number.

    In context

    The proof that the square root of two is irrational remains a fundamental exercise in introductory number theory.

  3. 03 C1 Advanced Technical Math

    n.a number that cannot be made by dividing two whole numbers.

    n.a real number that cannot be expressed as a quotient of two integers.

    Simple

    In this math problem, you need to identify which of these values are irrationals.

    In context

    The set of real numbers is composed of both rationals and irrationals, though the latter are far more numerous.

When we are convinced that someone is wrong, we may conclude that they are biased or irrational .

Phys.org· 15 Aug 2026

From Latin irratiōnālis, from ir- + ratiōnālis.

Etymology adapted from Wiktionary, available under CC BY-SA 4.0.

This entry
Origin Latin irratiōnālis
Level B2 · Upper Intermediate
Frequency Frequent
Updated