irrational
gb/ɪɹˈæʃənəl/ us/ɪɹˈæʃənəl/
B2
English
~ 8000
Senses
0 senses
adjective
B2
property
1
not reasonable or logical
Not based on clear thinking or good reasons; not reasonable.
Usage pattern:
to be irrational about [something]
Common mistake:
Learners sometimes think 'irrational' always means 'crazy' or 'mentally ill'. In everyday English, it mainly means 'not reasonable' or 'not logical', especially for actions, fears, and decisions. Also, some learners confuse this with the math meaning and think it always refers to numbers.
Synonyms
unreasonable (Very close in meaning; slightly more common and less formal.)
|
illogical (Focuses more on not following the rules of logic or clear thinking.)
|
senseless (Stronger and more emotional; suggests something is very stupid or pointless.)
Antonyms
rational (Emphasizes using clear, logical thought and good reasons.)
|
reasonable (Focuses on being fair, sensible, and based on good judgment.)
Collocations
irrational fear
|irrational behavior
|irrational decision
|irrational belief
|seem irrational
|completely irrational
Themes
thinking
|emotions
|daily life
|core_vocabulary
Examples
- Her fear of flying is completely irrational, especially since she has never had a bad experience on a plane.
- It would be irrational to quit your job before you find another one.
- He became irrational with jealousy and started accusing her of things she never did.
- The manager dismissed the complaint as irrational and not based on any facts.
- I know it sounds irrational, but I check the door three times before I can sleep.
Learner examples
- I have an irrational fear of dogs.
- It is irrational to drive so fast in the rain.
- He got angry in an irrational way.
- Her worry about small mistakes is irrational.
- They think buying that car now is irrational.
adjective
technical
C1
property
2
not expressible as a simple fraction
In math, about a number that you cannot write as one whole number over another whole number (a simple fraction).
Usage pattern:
an irrational [number]
Common mistake:
Learners sometimes mix the everyday meaning of 'irrational' (not logical) with the math meaning. In math, 'irrational' describes a type of number, not a bad or silly idea. Another mistake is to think that every number with many decimal places is irrational; some of them are still rational.
Synonyms
non-rational (Technical term used by some mathematicians; much less common in everyday teaching.)
Antonyms
rational (In mathematics, a number that can be written as a ratio of two integers.)
Collocations
irrational number
|pi is irrational
|prove that [x] is irrational
|square root of 2 is irrational
|show that [expression] is irrational
Themes
math
|science
|education
Examples
- We can prove that the square root of 2 is irrational.
- Pi is an irrational constant that appears in many formulas in geometry and physics.
- They asked the students to decide whether each number on the worksheet was rational or irrational.
- The teacher explained that an irrational number has an infinite, non-repeating decimal expansion.
- Because the result is irrational, it cannot be written exactly as a simple fraction.
Learner examples
- The square root of 2 is an irrational number.
- This decimal is irrational because it never ends and never repeats.
- In math class we learned the difference between rational and irrational numbers.
- Pi is the most famous irrational number.
- Not every square root is irrational.
Noun
technical
C1
entity
3
an irrational number (math)
In math, a number that you cannot write as one whole number over another whole number (a simple fraction).
Usage pattern:
an irrational [in a set of numbers]
Common mistake:
Learners often use the adjective form when a noun is needed, writing 'this is irrational number' instead of 'this is an irrational' or 'this is an irrational number'. The shortened noun form 'an irrational' is mostly used in math writing, so some learners may not recognize it as a noun.
Synonyms
irrational number (More explicit and slightly more common than the shortened form 'an irrational'.)
Antonyms
rational number (The contrasting set of real numbers that can be written as a ratio of two integers.)
Collocations
a rational or an irrational
|reals split into rationals and irrationals
|class of irrationals
|algebraic irrational
|transcendental irrational
Themes
math
|science
|education
Examples
- Within the real numbers, every number is either a rational or an irrational.
- The set of irrationals is uncountable, unlike the set of rationals.
- In this proof, we assume that the limit is an irrational and then derive a contradiction.
- They discussed whether the given decimal represented a rational or an irrational.
- Each root of the equation that is not a fraction is an irrational.
Learner examples
- Pi is an irrational.
- Zero point three three three is not an irrational.
- In this exercise, you must find one irrational.
- The teacher wrote two rationals and one irrational on the board.
- Not every square root is an irrational.
Grammar
Dictionary form
irrational
IPA
GB/ɪɹˈæʃənəl/
US/ɪɹˈæʃənəl/
Syllables & stress
ir - ra - tion - al (4 syllables)
Stress on 2nd syllable (ra)
Word forms
Adjective
- Base: irrational
Word family
Core family
irrationally
adverb
irrationality
noun
Negative and opposite forms
Advanced or less common
Expressions
irrational behavior
1/ɪɹˈæʃənəl bɪhˈeɪvjɚ/
fixed phrase
actions not based on reason
Actions that are not based on clear thinking or good reasons.
Examples
- The manager was fired for his repeated irrational behavior toward staff.
- Stress and lack of sleep can sometimes lead to irrational behavior.
- They were worried by his sudden irrational behavior during meetings.
irrational exuberance
1/ɪɹˈæʃənəl ɪɡzˈubɚəns/
fixed phrase
formal
overexcited, unjustified financial optimism
A very strong and excited belief, especially in financial markets, that prices will keep going up, even when there is no good reason.
Examples
- The central banker warned that stock prices might reflect irrational exuberance rather than real economic growth.
- Many analysts blamed the housing bubble on irrational exuberance among investors.
- Irrational exuberance pushed tech stocks far beyond their actual earnings.
irrational exuberance
1/ɪɹˈæʃənəl ɪɡzˈubɚəns/
fixed phrase
business
unrealistic market optimism
too much confidence that makes prices rise too high
Examples
- Some analysts warned that the surge in tech stocks was driven by irrational exuberance.
- The housing boom was later blamed on irrational exuberance and easy credit.
- After the crash, many investors admitted their decisions had been fueled by irrational exuberance.
irrational exuberance
1/ɪɹˈæʃənəl ɪɡzˈubɚəns/
fixed phrase
business
unreasonably excited optimism
Excitement and confidence that is not reasonable.
Examples
- Some economists blamed the bubble on irrational exuberance among investors.
- The CEO cautioned that irrational exuberance could push prices beyond their true value.
- After the bad news, a wave of irrational exuberance quickly disappeared.
irrational fear
1/ɪɹˈæʃənəl fˈɪɹ/
fixed phrase
a fear with no logical cause
A strong fear that is not based on real danger or good reasons.
Examples
- She has an irrational fear of elevators and will always take the stairs, even to the tenth floor.
- His irrational fear of failure stops him from trying new things.
- Therapy helped him understand where his irrational fear of water came from.
irrational number
1/ɪɹˈæʃənəl nˈʌmbɚ/
fixed phrase
technical
mathematical term for non-fractional real number
In math, a real number that you cannot write as one whole number over another whole number (a simple fraction).
Examples
- The teacher explained that the square root of 2 is an irrational number.
- Students must be able to tell whether a given decimal is a rational or an irrational number.
- Pi is the most famous irrational number in mathematics.