What does surd mean?
A surd is an irrational number or algebraic expression involving a root that cannot be simplified to a rational number. The familiar examples include √2, √3, and expressions such as 1 + √5, whose values cannot be written as fractions of integers. The term is especially associated with school mathematics, where students learn to simplify, rationalize, and combine surds. “Surd” is also used as an adjective, as in “surd expression” or “quadratic surd,” meaning that something involves irrational quantities. The word has an unusual history: it comes through Italian from Latin surdus, meaning “deaf,” and was applied to irrational roots because they seemed to lack the straightforward, intelligible character associated with rational numbers.
An irrational number or algebraic expression involving an irrational root, especially one that cannot be simplified into a rational number.
"The expression 5 + √2 is a surd."
Used mainly in mathematics, particularly in school algebra.
Relating to or involving an irrational number or root.
"The teacher asked the class to rationalize the surd denominator."
Common in mathematical combinations such as “surd expression,” “surd form,” and “quadratic surd.”
The plural is used for irrational numbers or expressions involving irrational roots.
"The exercise asks students to simplify several surds."
The word surd literally means “deaf,” because an irrational root was once imagined as a soundless or inexplicable mathematical quantity.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Where does surd come from?
The mathematical term entered English in the early 17th century from Italian surdo, meaning “deaf,” ultimately from Latin surdus, “deaf” or “sourd.” Mathematicians used the metaphor of deafness for algebraic quantities that could not be expressed as rational numbers or explained by the usual methods. The sense developed into the modern mathematical meanings “irrational number” and “root expression.”
Related word forms
How surd is actually used
Surd is primarily a formal mathematical term, especially common in British and Commonwealth education. In everyday language, “irrational number” is more widely understood.
Easily confused with surd
A square root is the number obtained when a quantity is multiplied by itself; a surd is an irrational value or expression involving a root, such as √2 or √3.
A radical is the root symbol or root expression itself, while a surd more specifically refers to an irrational number or expression containing one.