Radical symbol

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

${\displaystyle {\sqrt {x}},}$

while the nth root of x is written as

${\displaystyle {\sqrt[{n}]{x}}.}$

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

In

Principal square root

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 a 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.

Origin

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

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. The OpenType math table allows adding this overline following the radical symbol.

Legacy encodings of the square root character U+221A include:

• 0xC3 in Mac OS Roman and Mac OS Cyrillic
• 0xFB (Alt+251) in Code page 437 and Code page 866 (but not Code page 850) on DOS and the Windows console
• 0xD6 in the Symbol font encoding^[6]
• 02-69 (7-bit 0x2265,
  EUC 0xA2E5) in Japanese JIS X 0208^[7]
• 01-78 (
  EUC/UHC 0xA1EE) in Korean Wansung code^[8]
• 01-44 (
  EUC 0xA1CC) in Mainland Chinese GB 2312 or GBK^[9]
• Traditional Chinese: 0xA1D4 in
  EUC 0xA2B5 or 0x8EA1A2B5) in CNS 11643^[11][12]

The Symbol font displays the character without any vinculum whatsoever; the overline may be a separate character at 0x60.[13] The JIS,^[14] Wansung^[15] and CNS 11643^[11][16] code charts include a short overline attached to the radical symbol, whereas the GB 2312^[17] and GB 18030 charts do not.^[18]

Additionally a "Radical Symbol Bottom" (U+23B7, ⎷) is available in the

In LaTeX the square root symbol may be generated by the \sqrt macro,^[21] and the square root symbol without the overline may be generated by the \surd macro.^[22]

References