@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: a skos:ConceptScheme .
psr:-HXTWXBPR-5
  skos:prefLabel "nth root"@en, "racine d'un nombre"@fr ;
  a skos:Concept ;
  skos:narrower psr:-B334QQ74-4 .

psr:-B334QQ74-4
  skos:inScheme psr: ;
  skos:broader psr:-HXTWXBPR-5 ;
  dc:modified "2024-10-18"^^xsd:date ;
  skos:definition """En mathématiques, la <b>racine cubique</b> d'un nombre réel <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 y}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>y</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle y}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\\\\displaystyle y}"></span> est l'unique nombre réel <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 x}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>x</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle x}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/87f9e315fd7e2ba406057a97300593c4802b53e4" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.33ex; height:1.676ex;" alt="{\\\\displaystyle x}"></span> dont le cube (c'est-à-dire la puissance <abbr class="abbr" title="Troisième">3<sup>e</sup></abbr>) vaut <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 y}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>y</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle y}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\\\\displaystyle y}"></span> ; en d'autres termes, <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 y=x^{3}=x\\	imes x\\	imes x}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>y</mi>         <mo>=</mo>         <msup>           <mi>x</mi>           <mrow class="MJX-TeXAtom-ORD">             <mn>3</mn>           </mrow>         </msup>         <mo>=</mo>         <mi>x</mi>         <mo>×<!-- × --></mo>         <mi>x</mi>         <mo>×<!-- × --></mo>         <mi>x</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle y=x^{3}=x\\	imes x\\	imes x}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e5c5da6deb6f51212cc5af716ac891c2483717a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.406ex; height:3.009ex;" alt="{\\\\displaystyle y=x^{3}=x\\	imes x\\	imes x}"></span>. La racine cubique de <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 y}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mi>y</mi>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle y}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b8a6208ec717213d4317e666f1ae872e00620a0d" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:1.155ex; height:2.009ex;" alt="{\\\\displaystyle y}"></span> est notée <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}]{y}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mroot>             <mi>y</mi>             <mrow class="MJX-TeXAtom-ORD">               <mn>3</mn>             </mrow>           </mroot>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {\\\\sqrt[{3}]{y}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ab9483e263c52c959955e085a1f93502b8014cb4" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.171ex; width:3.091ex; height:3.009ex;" alt="{\\\\displaystyle {\\\\sqrt[{3}]{y}}}"></span>.  
<br/>(Wikipedia, L'Encylopédie Libre, <a href="https://fr.wikipedia.org/wiki/Racine_cubique">https://fr.wikipedia.org/wiki/Racine_cubique</a>)"""@fr, """In mathematics, a <b>cube root</b> of a number <span class="texhtml mvar" style="font-style:italic;">x</span> is a number <span class="texhtml mvar" style="font-style:italic;">y</span> such that <span class="texhtml"><i>y</i><sup>3</sup> = <i>x</i></span>.  All nonzero real numbers have exactly one real cube root and a pair of complex conjugate cube roots, and all nonzero complex numbers have three distinct complex cube roots.  For example, the real cube root of <span class="texhtml">8</span>, denoted <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}]{8}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mrow class="MJX-TeXAtom-ORD">           <mroot>             <mn>8</mn>             <mrow class="MJX-TeXAtom-ORD">               <mn>3</mn>             </mrow>           </mroot>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle {\\\\sqrt[{3}]{8}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/513fcbe75ae8a28fbf5b6a762df26f92fa74ff1a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\\\\displaystyle {\\\\sqrt[{3}]{8}}}"></span>, is <span class="texhtml">2</span>, because <span class="texhtml">2<sup>3</sup> = 8</span>, while the other cube roots of <span class="texhtml">8</span> are <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 -1+i{\\\\sqrt {3}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mo>−<!-- − --></mo>         <mn>1</mn>         <mo>+</mo>         <mi>i</mi>         <mrow class="MJX-TeXAtom-ORD">           <msqrt>             <mn>3</mn>           </msqrt>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle -1+i{\\\\sqrt {3}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e33b99c34816b92b11784a5812bad52e302743a" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.712ex; height:2.843ex;" alt="{\\\\displaystyle -1+i{\\\\sqrt {3}}}"></span> and <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 -1-i{\\\\sqrt {3}}}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mo>−<!-- − --></mo>         <mn>1</mn>         <mo>−<!-- − --></mo>         <mi>i</mi>         <mrow class="MJX-TeXAtom-ORD">           <msqrt>             <mn>3</mn>           </msqrt>         </mrow>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle -1-i{\\\\sqrt {3}}}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/9b35fb972f9f1fdbcca62ebd015435bf5959ced4" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.712ex; height:2.843ex;" alt="{\\\\displaystyle -1-i{\\\\sqrt {3}}}"></span>. The three cube roots of <span class="texhtml">−27<i>i</i></span> are:    <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 3i,\\\\quad {\\rac {3{\\\\sqrt {3}}}{2}}-{\\rac {3}{2}}i,\\\\quad {\\	ext{and}}\\\\quad -{\\rac {3{\\\\sqrt {3}}}{2}}-{\\rac {3}{2}}i.}">   <semantics>     <mrow class="MJX-TeXAtom-ORD">       <mstyle displaystyle="true" scriptlevel="0">         <mn>3</mn>         <mi>i</mi>         <mo>,</mo>         <mspace width="1em"></mspace>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mn>3</mn>               <mrow class="MJX-TeXAtom-ORD">                 <msqrt>                   <mn>3</mn>                 </msqrt>               </mrow>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>         <mo>−<!-- − --></mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>3</mn>             <mn>2</mn>           </mfrac>         </mrow>         <mi>i</mi>         <mo>,</mo>         <mspace width="1em"></mspace>         <mrow class="MJX-TeXAtom-ORD">           <mtext>and</mtext>         </mrow>         <mspace width="1em"></mspace>         <mo>−<!-- − --></mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mrow>               <mn>3</mn>               <mrow class="MJX-TeXAtom-ORD">                 <msqrt>                   <mn>3</mn>                 </msqrt>               </mrow>             </mrow>             <mn>2</mn>           </mfrac>         </mrow>         <mo>−<!-- − --></mo>         <mrow class="MJX-TeXAtom-ORD">           <mfrac>             <mn>3</mn>             <mn>2</mn>           </mfrac>         </mrow>         <mi>i</mi>         <mo>.</mo>       </mstyle>     </mrow>     <annotation encoding="application/x-tex">{\\\\displaystyle 3i,\\\\quad {\\rac {3{\\\\sqrt {3}}}{2}}-{\\rac {3}{2}}i,\\\\quad {\\	ext{and}}\\\\quad -{\\rac {3{\\\\sqrt {3}}}{2}}-{\\rac {3}{2}}i.}</annotation>   </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f416107769330c4b57b7fd7872525699750904a8" class="mwe-math-fallback-image-inline mw-invert" aria-hidden="true" style="vertical-align: -1.838ex; width:39.712ex; height:5.843ex;" alt="{\\\\displaystyle 3i,\\\\quad {\\rac {3{\\\\sqrt {3}}}{2}}-{\\rac {3}{2}}i,\\\\quad {\\	ext{and}}\\\\quad -{\\rac {3{\\\\sqrt {3}}}{2}}-{\\rac {3}{2}}i.}"> 
<br/>(Wikipedia, The Free Encyclopedia, <a href="https://en.wikipedia.org/wiki/Cube_root">https://en.wikipedia.org/wiki/Cube_root</a>)"""@en ;
  a skos:Concept ;
  skos:exactMatch <https://en.wikipedia.org/wiki/Cube_root>, <https://fr.wikipedia.org/wiki/Racine_cubique> ;
  skos:prefLabel "cube root"@en, "racine cubique"@fr .