U+221C was added to Unicode in version 1.1 (1993). It belongs to the block Mathematical Operators in the Basic Multilingual Plane.

This character is a Math Symbol and is commonly used, that is, in no specific script.

The glyph is not a composition. It has a Neutral East Asian Width. In bidirectional context it acts as Other Neutral and is mirrored. In text U+221C behaves as Alphabetic regarding line breaks. It has type Other for sentence and Other for word breaks. The Grapheme Cluster Break is Any.

The Wikipedia has the following information about this codepoint:

In mathematics, the

of a numbernth rootx, wherenis a positive integer, is a numberrwhich, when raised to the powernyieldsx

where

nis thedegreeof the root. A root of degree 2 is called asquare rootand a root of degree 3, acube root. Roots of higher degree are referred by using ordinal numbers, as infourth root,twentieth root, etc.For example:

- 2 is a square root of 4, since 2
^{2}= 4.- −2 is also a square root of 4, since (−2)
^{2}= 4.A real number or complex number has

nroots of degreen. While the roots of 0 are not distinct (all equaling 0), thennth roots of any other real or complex number are all distinct. Ifnis even andxis real and positive, one of itsnth roots is positive, one is negative, and the rest are complex but not real; ifnis even andxis real and negative, none of thenth roots is real. Ifnis odd andxis real, onenth root is real and has the same sign asx, while the other roots are not real. Finally, ifxis not real, then none of itsnth roots is real.Roots are usually written using the

radical symbolorradixor , with or denoting the square root, denoting the cube root, denoting the fourth root, and so on. In the expression ,nis called theindex, is theradical signorradix, andxis called theradicand. Since the radical symbol denotes a function, when a number is presented under the radical symbol it must return only one result, so a non-negative real root, called theprincipal, is preferred rather than others; if the only real root is negative, as for the cube root of –8, again the real root is considered the principal root. An unresolved root, especially one using the radical symbol, is often referred to as anth rootsurdor aradical. Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called aradical expression, and if it contains no transcendental functions or transcendental numbers it is called an algebraic expression.In calculus,

rootsare treated as special cases of exponentiation, where the exponent is a fraction:

Roots are particularly important in the theory of infinite series; the root test determines the radius of convergence of a power series.

Nth rootscan also be defined for complex numbers, and the complex roots of 1 (the roots of unity) play an important role in higher mathematics. Galois theory can be used to determine which algebraic numbers can be expressed using roots, and to prove the Abel-Ruffini theorem, which states that a general polynomial equation of degree five or higher cannot be solved using roots alone; this result is also known as "the insolubility of the quintic".

System | Representation |
---|---|

Nº | 8732 |

UTF-8 | E2 88 9C |

UTF-16 | 22 1C |

UTF-32 | 00 00 22 1C |

URL-Quoted | %E2%88%9C |

HTML-Escape | ∜ |

Wrong windows-1252 Mojibake | â |

Property | Value |
---|---|

Age (age) | 1.1 |

Unicode Name (na) | FOURTH ROOT |

Unicode 1 Name (na1) | — |

Block (blk) | Math_Operators |

General Category (gc) | Math Symbol |

Script (sc) | Common |

Bidirectional Category (bc) | Other Neutral |

Combining Class (ccc) | Not Reordered |

Decomposition Type (dt) | None |

Decomposition Mapping (dm) | |

Lowercase (Lower) | ✘ |

Simple Lowercase Mapping (slc) | |

Lowercase Mapping (lc) | |

Uppercase (Upper) | ✘ |

Simple Uppercase Mapping (suc) | |

Uppercase Mapping (uc) | |

Simple Titlecase Mapping (stc) | |

Titlecase Mapping (tc) | |

Case Folding (cf) | |

ASCII Hex Digit (AHex) | ✘ |

Alphabetic (Alpha) | ✘ |

Bidi Control (Bidi_C) | ✘ |

Bidi Mirrored (Bidi_M) | ✔ |

Bidi Paired Bracket (bpb) | |

Bidi Paired Bracket Type (bpt) | None |

Cased (Cased) | ✘ |

Composition Exclusion (CE) | ✘ |

Case Ignorable (CI) | ✘ |

Full Composition Exclusion (Comp_Ex) | ✘ |

Changes When Casefolded (CWCF) | ✘ |

Changes When Casemapped (CWCM) | ✘ |

Changes When NFKC Casefolded (CWKCF) | ✘ |

Changes When Lowercased (CWL) | ✘ |

Changes When Titlecased (CWT) | ✘ |

Changes When Uppercased (CWU) | ✘ |

Dash (Dash) | ✘ |

Deprecated (Dep) | ✘ |

Default Ignorable Code Point (DI) | ✘ |

Diacritic (Dia) | ✘ |

East Asian Width (ea) | Neutral |

Extender (Ext) | ✘ |

FC NFKC Closure (FC_NFKC) | |

Grapheme Cluster Break (GCB) | Any |

Grapheme Base (Gr_Base) | ✔ |

Grapheme Extend (Gr_Ext) | ✘ |

Grapheme Link (Gr_Link) | ✘ |

Hex Digit (Hex) | ✘ |

Hangul Syllable Type (hst) | Not Applicable |

Hyphen (Hyphen) | ✘ |

ID Continue (IDC) | ✘ |

Ideographic (Ideo) | ✘ |

ID Start (IDS) | ✘ |

IDS Binary Operator (IDSB) | ✘ |

IDS Trinary Operator and (IDST) | ✘ |

InMC (InMC) | — |

Indic Positional Category (InPC) | NA |

Indic Syllabic Category (InSC) | Other |

ISO 10646 Comment (isc) | — |

Joining Group (jg) | No_Joining_Group |

Join Control (Join_C) | ✘ |

Jamo Short Name (JSN) | — |

Joining Type (jt) | Non Joining |

Line Break (lb) | Alphabetic |

Logical Order Exception (LOE) | ✘ |

Math (Math) | ✔ |

Noncharacter Code Point (NChar) | ✘ |

NFC Quick Check (NFC_QC) | Yes |

NFD Quick Check (NFD_QC) | Yes |

NFKC Casefold (NFKC_CF) | |

NFKC Quick Check (NFKC_QC) | Yes |

NFKD Quick Check (NFKD_QC) | Yes |

Numeric Type (nt) | None |

Numeric Value (nv) | NaN |

Other Alphabetic (OAlpha) | ✘ |

Other Default Ignorable Code Point (ODI) | ✘ |

Other Grapheme Extend (OGr_Ext) | ✘ |

Other ID Continue (OIDC) | ✘ |

Other ID Start (OIDS) | ✘ |

Other Lowercase (OLower) | ✘ |

Other Math (OMath) | ✘ |

Other Uppercase (OUpper) | ✘ |

Pattern Syntax (Pat_Syn) | ✔ |

Pattern White Space (Pat_WS) | ✘ |

Quotation Mark (QMark) | ✘ |

Radical (Radical) | ✘ |

Sentence Break (SB) | Other |

Simple Case Folding (scf) | |

Script Extension (scx) | Common |

Soft Dotted (SD) | ✘ |

STerm (STerm) | ✘ |

Terminal Punctuation (Term) | ✘ |

Unified Ideograph (UIdeo) | ✘ |

Variation Selector (VS) | ✘ |

Word Break (WB) | Other |

White Space (WSpace) | ✘ |

XID Continue (XIDC) | ✘ |

XID Start (XIDS) | ✘ |

Expands On NFC (XO_NFC) | ✘ |

Expands On NFD (XO_NFD) | ✘ |

Expands On NFKC (XO_NFKC) | ✘ |

Expands On NFKD (XO_NFKD) | ✘ |