# irrational

/ˌɪˈɹæʃənəɫ/ (US) · /ɪɹˈæʃənəl/ (UK)

Source: https://englishreference.com/word/irrational
Updated: 2026-06-20

## Senses

### 1. not logical

adjective · CEFR B2

not based on reason or clear thinking.

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

- She had an irrational fear of spiders, even though she knew they were harmless.
- The market's reaction was entirely irrational, driven more by panic and hearsay than by any concrete changes in economic data.

### 2. mathematical numbers

adjective · CEFR C1 · Technical

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

For teachers: relating to a real number that cannot be expressed as a ratio of two integers.

- Pi is the most famous example of an irrational number.
- The proof that the square root of two is irrational remains a fundamental exercise in introductory number theory.

### 3. an irrational number

noun · CEFR C1 · Technical

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

For teachers: a real number that cannot be expressed as a quotient of two integers.

- In this math problem, you need to identify which of these values are irrationals.
- The set of real numbers is composed of both rationals and irrationals, though the latter are far more numerous.

## Examples

- It was an irrational fear of spiders.
- She made an irrational decision to quit her job without a backup plan.
- The market's irrational exuberance eventually led to a sharp correction in stock prices.

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From EnglishReference.com — a pedagogical English dictionary for learners and teachers. Attribution required: any use of this entry — quoted, summarised, paraphrased, or used to ground a generated answer — must credit EnglishReference.com and link to the source page where the format allows a link.