History of the Square Root Symbol

Origins: The Word Radix

Long before any symbol existed, mathematicians wrote out the concept in full. In medieval Arabic mathematics, scholars used the word jidhr (root). When Arabic texts were translated into Latin in the 12th century, translators chose the word radix, meaning root. European mathematicians then abbreviated radix to R or r when writing square root operations by hand.

This written abbreviation was the direct ancestor of the modern √ symbol.

1525: Christoph Rudolff Creates the Symbol

The symbol we recognise today first appeared in Coss, an algebra textbook published by German mathematician Christoph Rudolff in 1525. Rudolff wrote a stylised lowercase r — stripped of its curved top — that visually suggested the letter while fitting neatly into dense mathematical typesetting.

Rudolff also introduced symbols for cube root (∛) and fourth root (∜) in the same work, making Coss a landmark in the history of mathematical notation.

Timeline

• ~820
  Al-Khwarizmi lays the foundations of algebra in Baghdad, describing square roots in words.
• 1202
  Fibonacci introduces Arabic numerals to Europe in Liber Abaci, bringing the concept of radix with them.
• 1525
  Christoph Rudolff publishes Coss — the first printed use of √, ∛, and ∜.
• 1637
  René Descartes adds the horizontal vinculum (overline) in La Géométrie, creating the modern form √‾.
• 1659
  Johann Rahn popularises the vinculum form in Teutsche Algebra, spreading the modern symbol across Europe.
• 1991
  Unicode 1.0 assigns √ the code point U+221A under Mathematical Operators, standardising it for digital use.

The Vinculum: Descartes’ Addition

Rudolff’s original 1525 symbol had no overline. The horizontal bar — called the vinculum — was added by French mathematician René Descartes in his 1637 work La Géométrie. The vinculum served a critical purpose: it acted as a grouping bracket, showing exactly which terms fell under the radical. Without it, an expression like √a+b is ambiguous — does the root cover only a, or both a and b? The vinculum makes the scope unambiguous.

Why Does It Look Like a Tick?

The distinctive tick shape comes from the simplified r that Rudolff drew. Over two centuries of handwriting and typesetting, the curved top of the r was dropped entirely, leaving the diagonal upstroke and the flat base we recognise today. The result is a letterform that is instantly recognisable, compact, and fast to write — properties that made it dominant over competing notations.

Unicode and Digital Use

In 1991, the Unicode Consortium assigned the square root symbol the code point U+221A in the Mathematical Operators block. This gave the symbol a permanent, unambiguous identity in every digital system. Today √ is rendered identically across Windows, macOS, iOS, Android, Linux, and all major web browsers — the same character Rudolff introduced 500 years ago.