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Sqrt




Mathematica Notation

Traditional Notation









Elementary Functions > Sqrt[z] > Transformations > Products, sums, and powers of the direct function > Products of the direct function





http://functions.wolfram.com/01.01.16.0029.01









  


  








Input Form





Sqrt[Subscript[x, 1]] Sqrt[Subscript[x, 2]] == Sqrt[Subscript[x, 1] Subscript[x, 2]] /; (Subscript[x, 1] > 0 && Subscript[x, 2] > 0) || Subscript[x, 1] Subscript[x, 2] < 0








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SqrtBox[SubscriptBox["x", "1"]], " ", SqrtBox[SubscriptBox["x", "2"]]]], "\[Equal]", SqrtBox[RowBox[List[SubscriptBox["x", "1"], " ", SubscriptBox["x", "2"]]]]]], "/;", RowBox[List[RowBox[List[RowBox[List[SubscriptBox["x", "1"], ">", "0"]], " ", "\[And]", " ", RowBox[List[SubscriptBox["x", "2"], ">", "0"]]]], "\[Or]", RowBox[List[RowBox[List[SubscriptBox["x", "1"], " ", SubscriptBox["x", "2"]]], "<", "0"]]]]]]]]








MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <msqrt> <msub> <mi> x </mi> <mn> 1 </mn> </msub> </msqrt> <mo> &#8290; </mo> <msqrt> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </msqrt> </mrow> <mo> &#10869; </mo> <msqrt> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> </msqrt> </mrow> <mo> /; </mo> <mrow> <mrow> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> &gt; </mo> <mn> 0 </mn> </mrow> <mo> &#8743; </mo> <mrow> <msub> <mi> x </mi> <mn> 2 </mn> </msub> <mo> &gt; </mo> <mn> 0 </mn> </mrow> </mrow> <mo> &#8744; </mo> <mrow> <mrow> <msub> <mi> x </mi> <mn> 1 </mn> </msub> <mo> &#8290; </mo> <msub> <mi> x </mi> <mn> 2 </mn> </msub> </mrow> <mo> &lt; </mo> <mn> 0 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <power /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <or /> <apply> <and /> <apply> <gt /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 0 </cn> </apply> <apply> <gt /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> 0 </cn> </apply> </apply> <apply> <lt /> <apply> <times /> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 1 </cn> </apply> <apply> <ci> Subscript </ci> <ci> x </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 0 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SqrtBox[SubscriptBox["x_", "1"]], " ", SqrtBox[SubscriptBox["x_", "2"]]]], "]"]], "\[RuleDelayed]", RowBox[List[SqrtBox[RowBox[List[SubscriptBox["xx", "1"], " ", SubscriptBox["xx", "2"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SubscriptBox["xx", "1"], ">", "0"]], "&&", RowBox[List[SubscriptBox["xx", "2"], ">", "0"]]]], ")"]], "||", RowBox[List[RowBox[List[SubscriptBox["xx", "1"], " ", SubscriptBox["xx", "2"]]], "<", "0"]]]]]]]]]]


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





2001-10-29