What does biquadrate mean?
A biquadrate is the fourth power of a number or algebraic quantity — the value obtained by multiplying a quantity by itself four times, written as x⁴. The word combines the Latin prefix bi-, meaning 'twice', with 'quadrate', meaning 'to make square', reflecting the idea that a biquadrate is produced by squaring a number twice: squaring x gives x², and squaring that result gives x⁴. The term appeared in English mathematical writing from around the seventeenth century and was once standard in algebra instruction, alongside the related adjective 'biquadratic', which describes equations and expressions involving fourth powers, such as biquadratic equations. In contemporary usage, however, 'biquadrate' has largely fallen out of favor, replaced by the plainer phrase 'fourth power'; it persists mainly in historical mathematics texts, dictionaries, and vocabulary collections. For readers encountering older works on arithmetic or algebra, recognizing 'biquadrate' as simply another name for the fourth power is the key to understanding the text.
nounThe fourth power of a quantity — that is, the result of multiplying a number by itself four times (x⁴). The term is largely mathematical and somewhat archaic, having been largely supplanted in modern usage by 'fourth power' and 'biquadratic'.
- The fourth power of a number or quantity (x⁴); also called the biquadratic.
"Squaring the square of six yields its biquadrate, 1,296."
"To find the biquadrate of three, multiply three by itself twice more after squaring it, arriving at eighty-one."
"Early algebra texts required students to compute the biquadrate of various quantities by repeated multiplication."
The plural is used when referring to multiple fourth-power values or instances in mathematical discussion.
"The table listed the biquadrates of all integers up to twenty."
Before calculators made it trivial, raising a number to its biquadrate meant squaring it twice — a favorite exercise for generations of algebra students.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of biquadrate
Biquadrate derives from Latin roots: bi- meaning 'two' or 'twice', and quadratus, the past participle of quadrare, 'to make square', which itself stems from quadrus, 'a square', related to quattuor, 'four'. The term entered English in the early seventeenth century through mathematical treatises influenced by continental algebra, where powers beyond the cube were named systematically. It shares this Latin root with cognates such as 'quadrate', 'quadratic', 'quadrant', and 'quadruple', all ultimately tracing back to the Indo-European root for 'four'.
Related word forms
How biquadrate is actually used
Formal and technical register, now rare in everyday mathematics; modern texts overwhelmingly prefer 'fourth power'. The word survives chiefly in older textbooks, historical discussions of algebra, and specialized vocabulary lists.
Easily confused with biquadrate
'Biquadrate' is the noun denoting the fourth power itself, while 'biquadratic' is primarily an adjective describing expressions or equations involving the fourth power, such as a biquadratic equation.