Sqrt

Sqrt[z]
or gives the square root of z.

DetailsDetails

  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • can be entered using Ctrl+2 z or .
  • Sqrt[z] is converted to .
  • Sqrt[z^2] is not automatically converted to z.
  • Sqrt[a b] is not automatically converted to Sqrt[a]Sqrt[b].
  • These conversions can be done using PowerExpand, but will typically be correct only for positive real arguments.
  • For certain special arguments, Sqrt automatically evaluates to exact values.
  • Sqrt can be evaluated to arbitrary numerical precision.
  • Sqrt automatically threads over lists.
  • In StandardForm, Sqrt[z] is printed as .
  • z can also be used for input. The character is entered as EscsqrtEsc or \[Sqrt].

ExamplesExamplesopen allclose all

Basic Examples  (7)Basic Examples  (7)

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Evaluate numerically to any precision:

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Negative numbers have imaginary square roots:

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Sqrt threads element-wise over lists:

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is not automatically replaced by :

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It can be simplified to if one assumes :

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Enter using Ctrl+2:

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Introduced in 1988
(1.0)
| Updated in 1996
(3.0)