Root sign

Root sign
Root sign
	√∛
Specifications
Title	√ : square root; ∛ : cube root
Unicode	√ : U + 221A; ∛ : U + 221B
HTML code	√ : √ or √; ∛ : ∛ or ∛
Utf-16	√ : 0x221A; ∛ : 0x221B
Url	√ :% E2% 88% 9A; ∛ :% E2% 88% 9B
Mnemonics	√ : √

The sign of the root (the sign of the radical ) ( √ ) in mathematics is a symbol ${\sqrt {\quad }}$ ${\ displaystyle {\ sqrt {\ quad}}}$ ${\ sqrt {\ quad}}$ for roots , the default is square . In the general case (for roots of the nth degree), the exponent is placed above the “bird”: ${\sqrt[{3\,}]{\quad }}$ ${\ displaystyle {\ sqrt [{3 \,}] {\ quad}}}$ ${\ sqrt [{3 \,}] {\ quad}}$ used for cubic roots , ${\sqrt[{4\,}]{\quad }}$ ${\ displaystyle {\ sqrt [{4 \,}] {\ quad}}}$ ${\ sqrt [{4 \,}] {\ quad}}$ - for roots of the 4th degree, etc. for square root, you can also use the “full” notation ${\sqrt[{2\,}]{\quad }}$ ${\ displaystyle {\ sqrt [{2 \,}] {\ quad}}}$ ${\ sqrt [{2 \,}] {\ quad}}$ .

Content

History

The root sign comes from the lowercase Latin letter r (the initial Latin latin radix is the root), fused with a superscript: earlier, the overlay of the expression was used instead of its current conclusion in brackets. So that ${\sqrt {a+b}}$ ${\ displaystyle {\ sqrt {a + b}}}$ there’s just a modified way of writing an expression $\ r{\overline {a+b}}$ ${\ displaystyle \ r {\ overline {a + b}}}$ .

This designation was first used by the German mathematician Christoph Rudolph in 1525 . He also invented symbols. and for roots of the third and fourth degrees, respectively ^[1] .

Typography

american option
german version
Russian version ^[2]
TeX option

In some printing traditions (for example, in the Germanic), it is customary to supply the upper line of the root sign with a small serif facing down to the right. In American typography (in particular, the T _E Χ system ) this detail is not.

The length and height of the root sign must be such as to completely cover the radical expression. In the neighborhood of several root expressions of different (but close) heights in one line, it is often customary to adjust all the signs of the root to the highest of them.

The root sign is used only for expressions that fit within the string, and for longer ones instead ${\sqrt[{n\,}]{abcde\dots }}$ ${\ displaystyle {\ sqrt [{n \,}] {abcde \ dots}}}$ apply equivalent notation $(abcde\dots )^{1/n}$ ${\ displaystyle (abcde \ dots) ^ {1 / n}}$ . However, some typesetting and layout guides mention breaking a radical expression over several lines; in this case, the sign of the root is placed above the first, and a line is put above the continuation of the radical expression; at the place of line breaks, both the sign of the root and the line above the continuation are provided with arrows facing outward.

Notes

↑ Florian Cajori. A History Of Mathematical Notations. - The Open Court Company, 1928. - T. 1. - S. 150.
↑ Valentin Zaitsev, Andrew Janishewsky, Alexander Berdnikov: Russian Typographical Traditions in Mathematical Literature . In: EuroTeX'99 proceedings. Archived September 28, 2012 on the Wayback Machine (PDF 196 KB, english)

Literature

Florian Cajori: A History of Mathematical Notations (Two Volume in One) , Cosimo, 2011 (Nachdruck). ISBN 1-61640-571-6 .

[1] Florian Cajori. A History Of Mathematical Notations. - The Open Court Company, 1928. - T. 1. - S. 150.

[2] Valentin Zaitsev, Andrew Janishewsky, Alexander Berdnikov: Russian Typographical Traditions in Mathematical Literature . In: EuroTeX'99 proceedings. Archived September 28, 2012 on the Wayback Machine (PDF 196 KB, english)