surd

IPA/sɜːd/
IPA/sɜːrd/

surd — noun

1. a number that contains a root symbol (such as √2 or √3) and cannot be simplified

1.nounC2
Definition

a number that contains a root symbol (such as √2 or √3) and cannot be simplified to a whole number or a simple fraction; a root that does not produce a rational number.

Example

In algebra class, Leo had to simplify expressions that contained surds like 2√3.

collocation: simplify a surd

The square root of seven is a surd because its decimal form never ends or repeats.

Common collocations
  • simplify a surd
  • add surds
  • multiply surds
  • irrational surd
  • quadratic surd
Synonyms
  • irrational number

    broader category — all surds are irrational, but not all irrationals are surds

  • radical

    common informal term for the root expression itself (e.g. √3)

Antonyms

Grammar Patterns

a surd

the surd + noun

Usage Note

Often taught alongside rational and irrational numbers in high-school algebra. A surd is always an irrational number, but not every irrational number (such as π) is a surd — surds specifically involve roots.

Common Mistakes

Pi is a surd because its decimals never end.
Pi is an irrational number, but it is not a surd because it does not contain a root.
A surd is a specific type of irrational number that comes from a root.

2. a speech sound made without vibration of the vocal cords; a consonant such as p,

2.nounC2
Definition

a speech sound made without vibration of the vocal cords; a consonant such as p, t, or k that uses only the breath and not the voice.

Example

Abigail touched her throat and felt no vibration when she said the surd 'p'.

test: feel throat vibration for voiced vs surd

In phonetics class, Kenji listed the English surds: p, t, k, f, s, and others.

Common collocations
  • surd consonant
  • surd sound
  • produce a surd
  • voiceless surd
Synonyms
Antonyms
  • sonant

    a voiced sound produced with vocal cord vibration

  • voiced consonant

    a consonant like b, d, or g that uses the vocal cords

Grammar Patterns

a surd

surd + noun

Usage Note

Common in linguistics and language-teaching contexts. Most English voiceless stops (p, t, k) and fricatives (f, s, ʃ, θ) are surds. The opposite term is 'sonant' (a voiced sound).

Common Mistakes

The letter c is always a surd.
The letter c can represent the surd sound /k/ or the voiced sound /s/, depending on the word.
Letters are not surds; speech sounds are.

surd — adjective

Word family

  • surdity
    nounC2

Synonym discussion

Sense: noun/1

A surd is a specific type of irrational number that involves a root (such as √2 or √7). While every surd is an irrational number, the reverse is not true — π and e are irrational but are not surds because they are not derived from a root. A radical is the root symbol itself or the expression under it; for example, in √(x+3), the radical is √, and the entire expression may or may not be a surd depending on whether the result is irrational. In everyday math classes, 'surd' is used mainly when working with square roots and cube roots that cannot be simplified to whole numbers, while 'irrational number' covers the broader category of numbers with non-repeating, non-terminating decimals.

surd ↗irrational numberradical ↗

Etymology

LatinEnglish

The word 'surd' comes from the Latin 'surdus' meaning 'deaf' or 'muffled'. It entered English in the 16th century through mathematics, where it originally described numbers that were 'deaf' or 'silent' — that is, numbers that could not be expressed by a spoken ratio. By the 17th century it was also used in phonetics to describe sounds that the ear perceives as 'muffled' or lacking voice, because the vocal cords do not vibrate. The mathematical and phonetic meanings thus share the same root metaphor of something unheard or silent.

First known use

1610

1610, in the meaning defined at sense 1 Noun