Radical symbol

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In mathematics, the radical sign or radical symbol or root symbol is a symbol for the square root or higher-order root of a number. The square root of a number is written as

while the th root of is written as

It is also used for other meanings in more advanced mathematics, such as the radical of an ideal.

Principal square root[edit]

Technically, each positive real number has two square roots, one positive and the other negative. The square root symbol refers to the principal square root, which is the positive one. The two square roots of a negative number are both imaginary numbers, and the square root symbol refers to the principal square root, the one with positive imaginary part. For the definition of the principal square root of other complex numbers, see Square root#Principal square root of a complex number.


The origin of the root symbol √ is largely speculative. Some sources imply that the symbol was first used by Arab mathematicians. One of those mathematicians was Abū al-Hasan ibn Alī al-Qalasādī (1421–1486). Legend has it that it was taken from the Arabic letter "ج‎" (ǧīm, /im/), which is the first letter in the Arabic word "جذر‎" (jadhir, meaning "root"; /ˈɑːðir/).[1] However, many scholars, including Leonhard Euler,[2] believe it originates from the letter "r", the first letter of the Latin word "radix" (meaning "root"), referring to the same mathematical operation.

The symbol was first seen in print without the vinculum (the horizontal "bar" over the numbers inside the radical symbol) in the year 1525 in Die Coss by Christoff Rudolff, a German mathematician. In 1637 Descartes was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today.[3]


The Unicode and HTML character codes for the radical symbols are:

Read Character Unicode ASCII URL HTML (others)
Square root U+221A √ %E2%88%9A √
Cube root U+221B ∛ %E2%88%9B
Fourth root U+221C ∜ %E2%88%9C

However, these characters differ in appearance from most mathematical typesetting by omitting the overline connected to the radical symbol, which surrounds the argument of the square root function.

In LaTeX the square root symbol may be generated by the \sqrt macro, and the square root symbol without the overline may be generated by the \surd macro.


  1. ^ "Language Log: Ab surd". Retrieved 22 June 2012. 
  2. ^ Leonhard Euler (1755). Institutiones calculi differentialis (in Latin). 
  3. ^ Cajori, Florian (2012) [1928], A History of Mathematical Notations, I, Dover, p. 208, ISBN 978-0-486-67766-8