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Sqrt




Mathematica Notation

Traditional Notation









Elementary Functions > Sqrt[z] > Transformations > Nested direct and inverse functions





http://functions.wolfram.com/01.01.16.0039.01









  


  








Input Form





Sqrt[Sqrt[z^2 + 1] + z]/Sqrt[-z - Sqrt[z^2 + 1]] == (-Sqrt[-z]) Sqrt[1/z]








Standard Form





Cell[BoxData[RowBox[List[FractionBox[SqrtBox[RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]], "+", "z"]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", "z"]], "-", SqrtBox[RowBox[List[SuperscriptBox["z", "2"], "+", "1"]]]]]], " "]]], "\[Equal]", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["-", "z"]]]]], SqrtBox[FractionBox["1", "z"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mfrac> <msqrt> <mrow> <mi> z </mi> <mo> + </mo> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </msqrt> <msqrt> <mrow> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> - </mo> <msqrt> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> </mrow> </msqrt> </mfrac> <mo> &#10869; </mo> <mrow> <mrow> <mo> - </mo> <msqrt> <mrow> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> <mo> &#8290; </mo> <msqrt> <mfrac> <mn> 1 </mn> <mi> z </mi> </mfrac> </msqrt> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> z </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", FractionBox[SqrtBox[RowBox[List[SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]]], "+", "z_"]]], SqrtBox[RowBox[List[RowBox[List["-", "z_"]], "-", SqrtBox[RowBox[List[SuperscriptBox["z_", "2"], "+", "1"]]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SqrtBox[RowBox[List["-", "z"]]]]], " ", SqrtBox[FractionBox["1", "z"]]]]]]]]


Date Added to functions.wolfram.com (modification date)





2003-08-21