irrational number

Meaning

1. 1nouncountable

   A real number that cannot be written exactly as a ratio of two whole numbers.

   Grammar: Countable: pi and root two are irrational numbers. Do not confuse irrational here with unreasonable in everyday English.

   Patterns

   • prove a number is irrational
   • an irrational number such as pi
   • the set of irrational numbers
   • infinitely many irrational numbers

   Pi is an irrational number because its decimal never ends or repeats.

   The square root of two is irrational.

   Between any two rational numbers there are infinitely many irrational numbers.

Word forms

Common combinations

irrational number such as pi

Pi is the best-known irrational number such as pi used in geometry.

prove a number irrational

The class learned how to prove the square root of two irrational.

set of irrational numbers

The set of irrational numbers is uncountably infinite.

infinitely many irrational numbers

There are infinitely many irrational numbers on the number line.

Synonyms and how they differ

surd

A surd is an irrational root expression, especially in older school usage; irrational number is the broader modern term.

Opposites

Word family

irrational adjective

In math, not expressible as a ratio of integers; generally, not reasonable.

rational adjective

Expressible as a ratio of integers; generally, sensible.

Commonly confused: irrational number or irrational? irrational number or imaginary number?

Practice

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Write a sentence using “irrational number”, then check it and compare it with the examples above.

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