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Radical symbol - Wikipedia

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class="mw-page-title-main">Radical symbol</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="Go to an article in another language. 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href="https://be-tarask.wikipedia.org/wiki/%D0%97%D0%BD%D0%B0%D0%BA_%D0%BA%D0%BE%D1%80%D0%B0%D0%BD%D1%8F" title="Знак кораня – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Знак кораня" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Wurzelzeichen" title="Wurzelzeichen – German" lang="de" hreflang="de" data-title="Wurzelzeichen" data-language-autonym="Deutsch" data-language-local-name="German" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Juurem%C3%A4rk" title="Juuremärk – Estonian" lang="et" hreflang="et" data-title="Juuremärk" data-language-autonym="Eesti" data-language-local-name="Estonian" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EA%B7%BC%ED%98%B8" title="근호 – Korean" lang="ko" hreflang="ko" data-title="근호" data-language-autonym="한국어" data-language-local-name="Korean" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Radice_(simbolo)" title="Radice (simbolo) – Italian" lang="it" hreflang="it" data-title="Radice (simbolo)" data-language-autonym="Italiano" data-language-local-name="Italian" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A0%E1%83%90%E1%83%93%E1%83%98%E1%83%99%E1%83%90%E1%83%9A%E1%83%98_(%E1%83%9B%E1%83%90%E1%83%97%E1%83%94%E1%83%9B%E1%83%90%E1%83%A2%E1%83%98%E1%83%99%E1%83%90)" title="რადიკალი (მათემატიკა) – Georgian" lang="ka" hreflang="ka" data-title="რადიკალი (მათემატიკა)" data-language-autonym="ქართული" data-language-local-name="Georgian" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%A0%B9%E5%8F%B7" title="根号 – Japanese" lang="ja" hreflang="ja" data-title="根号" data-language-autonym="日本語" data-language-local-name="Japanese" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%97%D0%BD%D0%B0%D0%BA_%D0%BA%D0%BE%D1%80%D0%BD%D1%8F" title="Знак корня – Russian" lang="ru" hreflang="ru" data-title="Знак корня" data-language-autonym="Русский" data-language-local-name="Russian" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Rottecken" title="Rottecken – Swedish" lang="sv" hreflang="sv" data-title="Rottecken" data-language-autonym="Svenska" data-language-local-name="Swedish" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%AE%E0%AF%82%E0%AE%B2%E0%AE%95%E0%AF%8D_%E0%AE%95%E0%AF%81%E0%AE%B1%E0%AE%BF%E0%AE%AF%E0%AF%80%E0%AE%9F%E0%AF%81_(%E0%AE%95%E0%AE%A3%E0%AE%BF%E0%AE%A4%E0%AE%AE%E0%AF%8D)" title="மூலக் குறியீடு (கணிதம்) – Tamil" lang="ta" hreflang="ta" data-title="மூலக் குறியீடு (கணிதம்)" data-language-autonym="தமிழ்" data-language-local-name="Tamil" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B9%80%E0%B8%84%E0%B8%A3%E0%B8%B7%E0%B9%88%E0%B8%AD%E0%B8%87%E0%B8%AB%E0%B8%A1%E0%B8%B2%E0%B8%A2%E0%B8%81%E0%B8%A3%E0%B8%93%E0%B8%91%E0%B9%8C" title="เครื่องหมายกรณฑ์ – Thai" lang="th" hreflang="th" data-title="เครื่องหมายกรณฑ์" data-language-autonym="ไทย" data-language-local-name="Thai" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%97%D0%BD%D0%B0%D0%BA_%D0%BA%D0%BE%D1%80%D0%B5%D0%BD%D1%8F" title="Знак кореня – Ukrainian" lang="uk" hreflang="uk" data-title="Знак кореня" data-language-autonym="Українська" data-language-local-name="Ukrainian" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%A0%B9%E5%8F%B7" title="根号 – Chinese" lang="zh" hreflang="zh" data-title="根号" data-language-autonym="中文" data-language-local-name="Chinese" class="interlanguage-link-target"><span>中文</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q11536248#sitelinks-wikipedia" title="Edit 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class="mw-content-ltr mw-parser-output" lang="en" dir="ltr"><div class="shortdescription nomobile noexcerpt noprint searchaux" style="display:none">Mathematical symbol denoting a root</div> <style data-mw-deduplicate="TemplateStyles:r1236090951">.mw-parser-output .hatnote{font-style:italic}.mw-parser-output div.hatnote{padding-left:1.6em;margin-bottom:0.5em}.mw-parser-output .hatnote i{font-style:normal}.mw-parser-output .hatnote+link+.hatnote{margin-top:-0.5em}@media print{body.ns-0 .mw-parser-output .hatnote{display:none!important}}</style><div role="note" class="hatnote navigation-not-searchable">"Root symbol" redirects here. For the root symbols for gene and protein families, see <a href="/wiki/Gene_nomenclature#Symbol_and_name" title="Gene nomenclature">Gene nomenclature §&#160;Symbol and name</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">"√" redirects here. For the check symbol (✓), see <a href="/wiki/Check_mark" title="Check mark">Check mark</a>.</div> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1236090951"><div role="note" class="hatnote navigation-not-searchable">For symbols used by political radicals, see <a href="/wiki/List_of_ideological_symbols" title="List of ideological symbols">List of ideological symbols</a>.</div> <p>In mathematics, the <b>radical symbol</b>, <b>radical sign</b>, <b>root symbol</b>, <b>radix</b>, or <b>surd</b> is a <a href="/wiki/Mathematical_notation" title="Mathematical notation">symbol</a> for the <a href="/wiki/Square_root" title="Square root">square root</a> or <a href="/wiki/Nth_root" title="Nth root">higher-order root</a> of a number. The square root of a number <span class="texhtml"><i>x</i></span> is written as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt {x}},}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mi>x</mi> </msqrt> </mrow> <mo>,</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {x}},}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b9763d9ff8638b882608213f6dc8e9fc8ddc79d3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.912ex; height:3.009ex;" alt="{\displaystyle {\sqrt {x}},}"></span></dd></dl> <p>while the <span class="texhtml"><i>n</i></span>th root of <span class="texhtml"><i>x</i></span> is written as </p> <dl><dd><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle {\sqrt[{n}]{x}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mroot> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </mroot> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt[{n}]{x}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/8562e64a6bc6e408ddf67f055682c4dc9c9f957f" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.912ex; height:3.009ex;" alt="{\displaystyle {\sqrt[{n}]{x}}.}"></span></dd></dl> <p>It is also used for other meanings in more advanced mathematics, such as the <a href="/wiki/Radical_of_an_ideal" title="Radical of an ideal">radical of an ideal</a>. </p><p>In <a href="/wiki/Linguistics" title="Linguistics">linguistics</a>, the symbol is used to denote a <a href="/wiki/Root_word" class="mw-redirect" title="Root word">root word</a>. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Principal_square_root">Principal square root</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radical_symbol&amp;action=edit&amp;section=1" title="Edit section: Principal square root"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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 <a href="/wiki/Imaginary_number" title="Imaginary number">imaginary numbers</a>, 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 <a href="/wiki/Complex_number" title="Complex number">complex numbers</a>, see <a href="/wiki/Square_root#Principal_square_root_of_a_complex_number" title="Square root">Square root §&#160;Principal square root of a complex number</a>. </p> <div class="mw-heading mw-heading2"><h2 id="Origin">Origin</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radical_symbol&amp;action=edit&amp;section=2" title="Edit section: Origin"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>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 <a href="/wiki/Ab%C5%AB_al-Hasan_ibn_Al%C4%AB_al-Qalas%C4%81d%C4%AB" class="mw-redirect" title="Abū al-Hasan ibn Alī al-Qalasādī">Abū al-Hasan ibn Alī al-Qalasādī</a> (1421–1486). Legend has it that it was taken from the <a href="/wiki/Arabic" title="Arabic">Arabic</a> letter "<span title="Tajik-language text"><span lang="tg-Arab" dir="rtl">ج</span></span>" (<i><a href="/wiki/Gimel#Arabic_ǧīm" title="Gimel">ǧīm</a></i>), which is the first letter in the Arabic word "<span title="Tajik-language text"><span lang="tg-Arab" dir="rtl">جذر</span></span>" (<i>jadhir</i>, meaning "root").<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">&#91;</span>1<span class="cite-bracket">&#93;</span></a></sup> However, <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">&#91;</span>2<span class="cite-bracket">&#93;</span></a></sup> believed it originated from the letter "r", the first letter of the <a href="/wiki/Latin" title="Latin">Latin</a> word "<a href="/wiki/Radix" title="Radix">radix</a>" (meaning "root"), referring to the same <a href="/wiki/Operation_(mathematics)" title="Operation (mathematics)">mathematical operation</a>. </p><p>The symbol was first seen in print without the <a href="/wiki/Vinculum_(symbol)" title="Vinculum (symbol)">vinculum</a> (the horizontal "bar" over the numbers inside the radical symbol) in the year 1525 in <i>Die Coss</i> by <a href="/wiki/Christoff_Rudolff" class="mw-redirect" title="Christoff Rudolff">Christoff Rudolff</a>, a <a href="/wiki/German_people" class="mw-redirect" title="German people">German</a> mathematician. In 1637 <a href="/wiki/Renee_Descartes" class="mw-redirect" title="Renee Descartes">Descartes</a> was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">&#91;</span>3<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Encoding">Encoding</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radical_symbol&amp;action=edit&amp;section=3" title="Edit section: Encoding"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>The Unicode and HTML character codes for the radical symbols are: </p> <table class="wikitable" style="text-align:center;"> <tbody><tr> <th>Read</th> <th>Character</th> <th><a href="/wiki/Unicode" title="Unicode">Unicode</a><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">&#91;</span>4<span class="cite-bracket">&#93;</span></a></sup></th> <th><a href="/wiki/XML" title="XML">XML</a></th> <th><a href="/wiki/Uniform_Resource_Locator" class="mw-redirect" title="Uniform Resource Locator">URL</a></th> <th><a href="/wiki/HTML" title="HTML">HTML</a><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">&#91;</span>5<span class="cite-bracket">&#93;</span></a></sup> </th></tr> <tr> <td><i>Square root</i></td> <td>√</td> <td>U+221A</td> <td><code>&amp;#8730;</code> or <code>&amp;#x221A;</code></td> <td><code>%E2%88%9A</code></td> <td><code>&amp;radic;</code> or <code>&amp;Sqrt;</code> </td></tr> <tr> <td><i>Cube root</i></td> <td>∛</td> <td>U+221B</td> <td><code>&amp;#8731;</code> or <code>&amp;#x221B;</code></td> <td><code>%E2%88%9B</code></td> <td> </td></tr> <tr> <td><i>Fourth root</i></td> <td>∜</td> <td>U+221C</td> <td><code>&amp;#8732;</code> or <code>&amp;#x221C;</code></td> <td><code>%E2%88%9C</code></td> <td> </td></tr></tbody></table> <p>However, these characters differ in appearance from most mathematical typesetting by omitting the <a href="/wiki/Overline" title="Overline">overline</a> connected to the radical symbol, which surrounds the argument of the square root function. The <a href="/wiki/OpenType" title="OpenType">OpenType</a> math table allows adding this overline following the radical symbol. </p><p>Legacy encodings of the square root character U+221A include: </p> <ul><li>0xC3 in <a href="/wiki/Mac_OS_Roman" title="Mac OS Roman">Mac OS Roman</a> and <a href="/wiki/Mac_OS_Cyrillic_encoding" title="Mac OS Cyrillic encoding">Mac OS Cyrillic</a></li> <li>0xFB (<style data-mw-deduplicate="TemplateStyles:r1249182868">.mw-parser-output .keyboard-key{border:1px solid #aaa;border-radius:0.2em;box-shadow:0.1em 0.1em 0.2em rgba(0,0,0,0.1);background-color:var(--background-color-neutral-subtle,#f8f9fa);background-image:linear-gradient(to bottom,var(--background-color-neutral,#eaecf0),var(--background-color-neutral-subtle,#f8f9fa),var(--background-color-neutral,#eaecf0));color:var(--color-base,#202122);padding:0.1em 0.3em;font-family:inherit;font-size:0.85em}</style><kbd class="keyboard-key nowrap">Alt</kbd>+<link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">2</kbd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">5</kbd><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1249182868"><kbd class="keyboard-key nowrap">1</kbd>) in <a href="/wiki/Code_page_437" title="Code page 437">Code page 437</a> and <a href="/wiki/Code_page_866" title="Code page 866">Code page 866</a> (but not <a href="/wiki/Code_page_850" title="Code page 850">Code page 850</a>) on DOS and the Windows console</li> <li>0xD6 in the <a href="/wiki/Symbol_(typeface)" title="Symbol (typeface)">Symbol font encoding</a><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">&#91;</span>6<span class="cite-bracket">&#93;</span></a></sup></li> <li>02-69 (7-bit 0x2265, <a href="/wiki/Shift_JIS" title="Shift JIS">SJIS</a> 0x81E3, <a href="/wiki/EUC-JP" class="mw-redirect" title="EUC-JP">EUC</a> 0xA2E5) in Japanese <a href="/wiki/JIS_X_0208" title="JIS X 0208">JIS X 0208</a><sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">&#91;</span>7<span class="cite-bracket">&#93;</span></a></sup></li> <li>01-78 (<a href="/wiki/EUC-KR" class="mw-redirect" title="EUC-KR">EUC</a>/<a href="/wiki/Unified_Hangul_Code" title="Unified Hangul Code">UHC</a> 0xA1EE) in Korean <a href="/wiki/KS_X_1001" title="KS X 1001">Wansung code</a><sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">&#91;</span>8<span class="cite-bracket">&#93;</span></a></sup></li> <li>01-44 (<a href="/wiki/EUC-CN" class="mw-redirect" title="EUC-CN">EUC</a> 0xA1CC) in Mainland Chinese <a href="/wiki/GB_2312" title="GB 2312">GB 2312</a> or <a href="/wiki/GBK_(character_encoding)" title="GBK (character encoding)">GBK</a><sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">&#91;</span>9<span class="cite-bracket">&#93;</span></a></sup></li> <li>Traditional Chinese: 0xA1D4 in <a href="/wiki/Big5" title="Big5">Big5</a><sup id="cite_ref-10" class="reference"><a href="#cite_note-10"><span class="cite-bracket">&#91;</span>10<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-cnstwradic_11-0" class="reference"><a href="#cite_note-cnstwradic-11"><span class="cite-bracket">&#91;</span>11<span class="cite-bracket">&#93;</span></a></sup> or 1-2235 (kuten 01-02-21, <a href="/wiki/EUC-TW" class="mw-redirect" title="EUC-TW">EUC</a> 0xA2B5 or 0x8EA1A2B5) in <a href="/wiki/CNS_11643" title="CNS 11643">CNS 11643</a><sup id="cite_ref-cnstwradic_11-1" class="reference"><a href="#cite_note-cnstwradic-11"><span class="cite-bracket">&#91;</span>11<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">&#91;</span>12<span class="cite-bracket">&#93;</span></a></sup></li></ul> <p>The Symbol font displays the character without any vinculum whatsoever; the overline may be a separate character at 0x60.<sup id="cite_ref-13" class="reference"><a href="#cite_note-13"><span class="cite-bracket">&#91;</span>13<span class="cite-bracket">&#93;</span></a></sup> The JIS,<sup id="cite_ref-14" class="reference"><a href="#cite_note-14"><span class="cite-bracket">&#91;</span>14<span class="cite-bracket">&#93;</span></a></sup> Wansung<sup id="cite_ref-15" class="reference"><a href="#cite_note-15"><span class="cite-bracket">&#91;</span>15<span class="cite-bracket">&#93;</span></a></sup> and CNS 11643<sup id="cite_ref-cnstwradic_11-2" class="reference"><a href="#cite_note-cnstwradic-11"><span class="cite-bracket">&#91;</span>11<span class="cite-bracket">&#93;</span></a></sup><sup id="cite_ref-16" class="reference"><a href="#cite_note-16"><span class="cite-bracket">&#91;</span>16<span class="cite-bracket">&#93;</span></a></sup> code charts include a short overline attached to the radical symbol, whereas the GB 2312<sup id="cite_ref-17" class="reference"><a href="#cite_note-17"><span class="cite-bracket">&#91;</span>17<span class="cite-bracket">&#93;</span></a></sup> and <a href="/wiki/GB_18030" title="GB 18030">GB 18030</a> charts do not.<sup id="cite_ref-18" class="reference"><a href="#cite_note-18"><span class="cite-bracket">&#91;</span>18<span class="cite-bracket">&#93;</span></a></sup> </p><p>Additionally a "Radical Symbol Bottom" (U+23B7, ⎷) is available in the <a href="/wiki/Miscellaneous_Technical" title="Miscellaneous Technical">Miscellaneous Technical</a> block.<sup id="cite_ref-19" class="reference"><a href="#cite_note-19"><span class="cite-bracket">&#91;</span>19<span class="cite-bracket">&#93;</span></a></sup> This was used in contexts where <a href="/wiki/Box-drawing_character" class="mw-redirect" title="Box-drawing character">box-drawing characters</a> are used, such as in the <a href="/wiki/DEC_Technical_Character_Set" title="DEC Technical Character Set">technical character set</a> of <a href="/wiki/Digital_Equipment_Corporation" title="Digital Equipment Corporation">DEC</a> terminals, to join up with box drawing characters on the line above to create the vinculum.<sup id="cite_ref-20" class="reference"><a href="#cite_note-20"><span class="cite-bracket">&#91;</span>20<span class="cite-bracket">&#93;</span></a></sup> </p><p>In <a href="/wiki/LaTeX" title="LaTeX">LaTeX</a> the square root symbol may be generated by the <code>\sqrt</code> macro,<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">&#91;</span>21<span class="cite-bracket">&#93;</span></a></sup> and the square root symbol without the overline may be generated by the <code>\surd</code> macro.<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">&#91;</span>22<span class="cite-bracket">&#93;</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="References">References</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Radical_symbol&amp;action=edit&amp;section=4" title="Edit section: References"><span>edit</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r1239543626">.mw-parser-output .reflist{margin-bottom:0.5em;list-style-type:decimal}@media screen{.mw-parser-output .reflist{font-size:90%}}.mw-parser-output .reflist .references{font-size:100%;margin-bottom:0;list-style-type:inherit}.mw-parser-output .reflist-columns-2{column-width:30em}.mw-parser-output .reflist-columns-3{column-width:25em}.mw-parser-output .reflist-columns{margin-top:0.3em}.mw-parser-output .reflist-columns ol{margin-top:0}.mw-parser-output .reflist-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .reflist-upper-alpha{list-style-type:upper-alpha}.mw-parser-output .reflist-upper-roman{list-style-type:upper-roman}.mw-parser-output .reflist-lower-alpha{list-style-type:lower-alpha}.mw-parser-output .reflist-lower-greek{list-style-type:lower-greek}.mw-parser-output .reflist-lower-roman{list-style-type:lower-roman}</style><div class="reflist"> <div class="mw-references-wrap mw-references-columns"><ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><style data-mw-deduplicate="TemplateStyles:r1238218222">.mw-parser-output cite.citation{font-style:inherit;word-wrap:break-word}.mw-parser-output .citation q{quotes:"\"""\"""'""'"}.mw-parser-output .citation:target{background-color:rgba(0,127,255,0.133)}.mw-parser-output .id-lock-free.id-lock-free a{background:url("//upload.wikimedia.org/wikipedia/commons/6/65/Lock-green.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-limited.id-lock-limited a,.mw-parser-output .id-lock-registration.id-lock-registration a{background:url("//upload.wikimedia.org/wikipedia/commons/d/d6/Lock-gray-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .id-lock-subscription.id-lock-subscription a{background:url("//upload.wikimedia.org/wikipedia/commons/a/aa/Lock-red-alt-2.svg")right 0.1em center/9px no-repeat}.mw-parser-output .cs1-ws-icon a{background:url("//upload.wikimedia.org/wikipedia/commons/4/4c/Wikisource-logo.svg")right 0.1em center/12px no-repeat}body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-free a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-limited a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-registration a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .id-lock-subscription a,body:not(.skin-timeless):not(.skin-minerva) .mw-parser-output .cs1-ws-icon a{background-size:contain;padding:0 1em 0 0}.mw-parser-output .cs1-code{color:inherit;background:inherit;border:none;padding:inherit}.mw-parser-output .cs1-hidden-error{display:none;color:var(--color-error,#d33)}.mw-parser-output .cs1-visible-error{color:var(--color-error,#d33)}.mw-parser-output .cs1-maint{display:none;color:#085;margin-left:0.3em}.mw-parser-output .cs1-kern-left{padding-left:0.2em}.mw-parser-output .cs1-kern-right{padding-right:0.2em}.mw-parser-output .citation .mw-selflink{font-weight:inherit}@media screen{.mw-parser-output .cs1-format{font-size:95%}html.skin-theme-clientpref-night .mw-parser-output .cs1-maint{color:#18911f}}@media screen and (prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .cs1-maint{color:#18911f}}</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="http://itre.cis.upenn.edu/~myl/languagelog/archives/002662.html">"Language Log: <i>Ab surd</i>"</a><span class="reference-accessdate">. Retrieved <span class="nowrap">22 June</span> 2012</span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=Language+Log%3A+Ab+surd&amp;rft_id=http%3A%2F%2Fitre.cis.upenn.edu%2F~myl%2Flanguagelog%2Farchives%2F002662.html&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ARadical+symbol" class="Z3988"></span></span> </li> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFLeonhard_Euler1755" class="citation book cs1 cs1-prop-foreign-lang-source">Leonhard Euler (1755). <a rel="nofollow" class="external text" href="https://archive.org/details/bub_gb_sYE_AAAAcAAJ"><i>Institutiones calculi differentialis</i></a> (in Latin). Petropolis.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=Institutiones+calculi+differentialis&amp;rft.pub=Petropolis&amp;rft.date=1755&amp;rft.au=Leonhard+Euler&amp;rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fbub_gb_sYE_AAAAcAAJ&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ARadical+symbol" class="Z3988"></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFCajori2012" class="citation book cs1">Cajori, Florian (2012) [1928]. <span class="id-lock-registration" title="Free registration required"><a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema00cajo_0/page/208"><i>A History of Mathematical Notations</i></a></span>. Vol.&#160;I. Dover. p.&#160;<a rel="nofollow" class="external text" href="https://archive.org/details/historyofmathema00cajo_0/page/208">208</a>. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&#160;<a href="/wiki/Special:BookSources/978-0-486-67766-8" title="Special:BookSources/978-0-486-67766-8"><bdi>978-0-486-67766-8</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=book&amp;rft.btitle=A+History+of+Mathematical+Notations&amp;rft.pages=208&amp;rft.pub=Dover&amp;rft.date=2012&amp;rft.isbn=978-0-486-67766-8&amp;rft.aulast=Cajori&amp;rft.aufirst=Florian&amp;rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryofmathema00cajo_0%2Fpage%2F208&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ARadical+symbol" class="Z3988"></span></span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFUnicode_Consortium2022" class="citation web cs1">Unicode Consortium (2022-09-16). <a rel="nofollow" class="external text" href="https://www.unicode.org/charts/PDF/U2200.pdf">"Mathematical Operators"</a> <span class="cs1-format">(PDF)</span>. <i>The Unicode Standard</i> (15.0&#160;ed.)<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-07-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&amp;rft.genre=unknown&amp;rft.jtitle=The+Unicode+Standard&amp;rft.atitle=Mathematical+Operators&amp;rft.date=2022-09-16&amp;rft.au=Unicode+Consortium&amp;rft_id=https%3A%2F%2Fwww.unicode.org%2Fcharts%2FPDF%2FU2200.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ARadical+symbol" class="Z3988"></span></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFWeb_Hypertext_Application_Technology_Working_Group2023" class="citation web cs1">Web Hypertext Application Technology Working Group (2023-07-14). <a rel="nofollow" class="external text" href="https://html.spec.whatwg.org/multipage/named-characters.html">"Named Character References"</a>. <i>HTML Living Standard</i><span class="reference-accessdate">. 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Retrieved <span class="nowrap">2023-07-16</span></span>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=unknown&amp;rft.btitle=The+LATEX+2%CE%B5+Sources&amp;rft.pages=%C2%A7+ltmath.dtx%3A+Math+Environments&amp;rft.edition=2023-06-01+Patch+Level+1&amp;rft.date=2023-06-01&amp;rft.aulast=Braams&amp;rft.aufirst=Johannes&amp;rft.au=Carlisle%2C+David&amp;rft.au=Jeffrey%2C+Alan&amp;rft.au=Lamport%2C+Leslie&amp;rft.au=Mittelbach%2C+Frank&amp;rft.au=Rowley%2C+Chris&amp;rft.au=Sch%C3%B6pf%2C+Rainer&amp;rft_id=http%3A%2F%2Fmirrors.ctan.org%2Fmacros%2Flatex%2Fbase%2Fsource2e.pdf&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ARadical+symbol" class="Z3988"></span></span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r1238218222"><cite id="CITEREFGrätzer2014" class="citation book cs1">Grätzer, George (2014). <a rel="nofollow" class="external text" href="https://books.google.com/books?id=BxhRBAAAQBAJ&amp;pg=PA172">"Table B.5: Miscellaneous symbols"</a>. <i>Practical LaTeX</i>. Springer. p.&#160;172. <a href="/wiki/ISBN_(identifier)" class="mw-redirect" title="ISBN (identifier)">ISBN</a>&#160;<a href="/wiki/Special:BookSources/9783319064253" title="Special:BookSources/9783319064253"><bdi>9783319064253</bdi></a>.</cite><span title="ctx_ver=Z39.88-2004&amp;rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook&amp;rft.genre=bookitem&amp;rft.atitle=Table+B.5%3A+Miscellaneous+symbols&amp;rft.btitle=Practical+LaTeX&amp;rft.pages=172&amp;rft.pub=Springer&amp;rft.date=2014&amp;rft.isbn=9783319064253&amp;rft.aulast=Gr%C3%A4tzer&amp;rft.aufirst=George&amp;rft_id=https%3A%2F%2Fbooks.google.com%2Fbooks%3Fid%3DBxhRBAAAQBAJ%26pg%3DPA172&amp;rfr_id=info%3Asid%2Fen.wikipedia.org%3ARadical+symbol" class="Z3988"></span></span> </li> </ol></div></div> <div class="navbox-styles"><style data-mw-deduplicate="TemplateStyles:r1129693374">.mw-parser-output .hlist dl,.mw-parser-output .hlist ol,.mw-parser-output .hlist ul{margin:0;padding:0}.mw-parser-output .hlist dd,.mw-parser-output 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navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:Navbox_punctuation" title="Template:Navbox punctuation"><abbr title="View this template">v</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:Navbox_punctuation" title="Template talk:Navbox punctuation"><abbr title="Discuss this template">t</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:EditPage/Template:Navbox_punctuation" title="Special:EditPage/Template:Navbox punctuation"><abbr title="Edit this template">e</abbr></a></li></ul></div><div id="Common_punctuation_and_other_typographical_symbols" style="font-size:114%;margin:0 4em">Common <a href="/wiki/Punctuation" title="Punctuation">punctuation</a> and other <a href="/wiki/Typography" title="Typography">typographical</a> symbols</div></th></tr><tr><td colspan="2" class="navbox-list navbox-odd" style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap">&#160;<span style="background: var( 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style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap">&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;-&#8201;</span>&#8201;&#160;<span style="font-size:95%"><a href="/wiki/Hyphen-minus" title="Hyphen-minus">hyphen-minus</a></span></span>&#160;</li> <li><span class="nowrap">&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;‒&#8201;</span>&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;–&#8201;</span>&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;—&#8201;</span>&#8201;&#160;<span style="font-size:95%"><a href="/wiki/Dash" title="Dash">dash</a></span></span>&#160;</li> <li><span class="nowrap">&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: 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title="Exclamation mark">exclamation mark</a></span></span>&#160;</li> <li><span class="nowrap">&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;‽&#8201;</span>&#8201;&#160;<span style="font-size:95%"><a href="/wiki/Interrobang" title="Interrobang">interrobang</a></span></span>&#160;</li> <li><span class="nowrap">&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;¡&#8201;</span>&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;¿&#8201;</span>&#8201;&#160;<span style="font-size:95%"><a href="/wiki/Inverted_question_and_exclamation_marks" class="mw-redirect" title="Inverted question and exclamation marks">inverted&#160;! and&#160;?</a></span></span>&#160;</li> <li><span class="nowrap">&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; 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style="width:100%;padding:0;text-align:left;"><div style="padding:0 0.25em"> <ul><li><span class="nowrap">&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;‘&#160;’&#8201;</span>&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;“&#160;”&#8201;</span>&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;'&#160;'&#8201;</span>&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;"&#160;"&#8201;</span>&#8201;&#160;<span style="font-size:95%"><a href="/wiki/Quotation_mark" title="Quotation mark">quotation mark</a></span></span>&#160;</li> <li><span class="nowrap">&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;‹&#160;›&#8201;</span>&#160;<span style="background: var( 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var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;⸿&#8201;</span>&#8201;&#160;<span style="font-size:95%"><a href="/wiki/Pilcrow" title="Pilcrow">pilcrow</a> (paragraph mark)</span></span>&#160;</li> <li><span class="nowrap">&#160;<span style="background: var( --background-color-neutral, #eaecf0 ); color: inherit; font-size:125%;">&#8201;§&#8201;</span>&#8201;&#160;<span style="font-size:95%"><a href="/wiki/Section_sign" title="Section sign">section mark</a></span></span>&#160;</li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="2"><div> <ul><li><a href="/wiki/List_of_typographical_symbols_and_punctuation_marks" title="List of typographical symbols and punctuation marks">Version of this table as a sortable list</a></li></ul> <ul><li><a href="/wiki/Currency_symbol" title="Currency symbol">Currency symbols</a></li> <li><a href="/wiki/Diacritic" title="Diacritic">Diacritics</a> (accents)</li> <li><a href="/wiki/List_of_logic_symbols" title="List of logic symbols">Logic symbols</a></li> <li><a href="/wiki/List_of_mathematical_symbols" class="mw-redirect" title="List of mathematical symbols">Math symbols</a></li> <li><a href="/wiki/Whitespace_character" title="Whitespace character">Whitespace</a></li></ul> <ul><li><a href="/wiki/Chinese_punctuation" title="Chinese punctuation">Chinese punctuation</a></li> <li><a href="/wiki/Hebrew_punctuation" title="Hebrew punctuation">Hebrew punctuation</a></li> <li><a href="/wiki/Japanese_punctuation" title="Japanese punctuation">Japanese punctuation</a></li> <li><a href="/wiki/Korean_punctuation" title="Korean punctuation">Korean punctuation</a></li></ul> </div></td></tr></tbody></table></div> <!-- NewPP limit report Parsed by mw‐web.codfw.main‐f69cdc8f6‐6f8kn Cached time: 20241122145300 Cache expiry: 2592000 Reduced expiry: false Complications: [vary‐revision‐sha1, show‐toc] CPU time usage: 0.725 seconds Real time usage: 0.934 seconds Preprocessor visited node count: 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