@prefix psr: <http://data.loterre.fr/ark:/67375/PSR> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .
@prefix dc: <http://purl.org/dc/terms/> .
@prefix xsd: <http://www.w3.org/2001/XMLSchema#> .

psr:-Z5HH6H12-K
  skos:prefLabel "racine carrée"@fr, "square root"@en ;
  a skos:Concept ;
  skos:broader psr:-HXTWXBPR-5 .

psr:-HXTWXBPR-5
  skos:definition """En mathématiques, une <b> racine <span class="texhtml"><i>n</i></span>-ième d'un nombre</b> <span class="texhtml"><i>a</i></span> est un nombre <span class="texhtml"><i>b</i></span> tel que <span class="texhtml"><i>b<sup>n</sup> = a</i></span>, où <span class="texhtml"><i>n</i></span> est un entier naturel non nul. Selon que l'on travaille dans l'ensemble des réels positifs, l'ensemble des réels ou l'ensemble des complexes, le nombre de racines <span class="texhtml"><i>n</i></span>-ièmes d'un nombre peut être 0, 1, 2 ou <span class="texhtml"><i>n</i></span>. Pour un nombre réel <span class="texhtml"><i>a</i></span> positif, il existe un unique réel <span class="texhtml"><i>b</i></span> positif tel que <span class="texhtml"><i>b<sup>n</sup> = a</i></span>. Ce réel est appelé <b>la racine <span class="texhtml"><i>n</i></span>-ième de <span class="texhtml"><i>a</i></span></b> (ou <b>racine <i>n</i>-ième principale</b> de <span class="texhtml"><i>a</i></span>) et se note <span class="racine texhtml"><sup style="margin-right: -0.5em; vertical-align: 0.8em;"><i>n</i></sup>√<span style="border-top:1px solid; padding:0 0.1em;"><i>a</i></span></span> avec le symbole <b>radical</b> (<span class="racine texhtml">√<span style="border-top:1px solid; padding:0 0.1em;"> </span></span>) ou <span class="texhtml"><i>a</i><sup>1/<i>n</i></sup></span>. La racine la plus connue est la racine carrée d'un réel. Cette définition se généralise pour <span class="texhtml"><i>a</i></span> négatif et <span class="texhtml"><i>b</i></span> négatif à condition que <span class="texhtml"><i>n</i></span> soit impair. Le terme de racine d'un nombre ne doit pas être confondu avec celui de racine d'un polynôme qui désigne la (ou les) valeur(s) où le polynôme s'annule. 
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Racine_d%27un_nombre">https://fr.wikipedia.org/wiki/Racine_d%27un_nombre</a>)"""@fr, """In mathematics, taking the <b><i>n</i>th</b> root is an operation involving two numbers, the <i>radicand</i> and the <i>index</i> or <i>degree</i>. Taking the nth root is written as <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>       </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/7b3ba2638d05cd9ed8dafae7e34986399e48ea99" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.266ex; height:3.009ex;" alt="{\\\\displaystyle {\\\\sqrt[{n}]{x}}}"></span>, where <span class="texhtml mvar" style="font-style:italic;">x</span> is the radicand and <i>n</i> is the index (also sometimes called the degree). This is pronounced as "the nth root of x". The definition then of an <b><i>n</i>th root</b> of a number <i>x</i> is a number <i>r</i> (the root) which, when raised to the power of the positive integer <i>n</i>, yields <i>x</i>:  <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 r^{n}=x.}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <msup>           <mi>r</mi>           <mrow class="MJX-TeXAtom-ORD">             <mi>n</mi>           </mrow>         </msup>         <mo>=</mo>         <mi>x</mi>         <mo>.</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle r^{n}=x.}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/e193fe7a53ebc7310d4ca7c0b9bbdb6b262af50f" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:7.342ex; height:2.343ex;" alt="{\\\\displaystyle r^{n}=x.}"></span></dd></dl> A root of degree 2 is called a <i>square root</i> (usually written without the <i>n</i> as just <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>       </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/d62b24be305beff66cba9bfbcc01a362ba390f44" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.266ex; height:3.009ex;" alt="{\\\\displaystyle {\\\\sqrt {x}}}"></span>) and a root of degree 3, a <i>cube root</i> (written <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[{3}]{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">               <mn>3</mn>             </mrow>           </mroot>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {\\\\sqrt[{3}]{x}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9a55f866116e7a86823816615dd98fcccde75473" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.005ex; width:3.266ex; height:3.009ex;" alt="{\\\\displaystyle {\\\\sqrt[{3}]{x}}}"></span>). Roots of higher degree are referred by using ordinal numbers, as in <i>fourth root</i>, <i>twentieth root</i>, etc.  The computation of an <span class="texhtml"><i>n</i></span>th root is a <b>root extraction</b>. 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Nth_root">https://en.wikipedia.org/wiki/Nth_root</a>)"""@en ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Racine_d%27un_nombre>, <https://en.wikipedia.org/wiki/Nth_root> ;
  skos:inScheme psr: ;
  skos:narrower psr:-TXRS2VPR-R, psr:-B334QQ74-4, psr:-Z5HH6H12-K ;
  skos:altLabel "racine n-ième d'un nombre"@fr ;
  skos:broader psr:-R556XDWR-W ;
  a skos:Concept ;
  skos:prefLabel "nth root"@en, "racine d'un nombre"@fr ;
  dc:modified "2024-10-18"^^xsd:date .

psr:-B334QQ74-4
  skos:prefLabel "racine cubique"@fr, "cube root"@en ;
  a skos:Concept ;
  skos:broader psr:-HXTWXBPR-5 .

psr: a skos:ConceptScheme .
psr:-R556XDWR-W
  skos:prefLabel "algebraic operation"@en, "opération algébrique"@fr ;
  a skos:Concept ;
  skos:narrower psr:-HXTWXBPR-5 .

psr:-TXRS2VPR-R
  skos:prefLabel "racine de l'unité"@fr, "root of unity"@en ;
  a skos:Concept ;
  skos:broader psr:-HXTWXBPR-5 .