This article provides square root equation examples for LibreOffice Math. you can copy and run all codes here in Math, and also use in Writer documents. At the end, you can download the document examples (.odf & .odt) you can study & edit later. This article is a part of LibreOffice Math the series here (Getting started, Matrix, Integral, Limit, and Trigonometry). I hope this article will be helpful for teachers in using LibreOffice at schools.

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Example 1


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nroot{n}{a} = a^{ 1 over n }
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nroot{ n }{ a^m } = a^{ m over n }
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sqrt{ 9 } = 3 ...
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Example 2


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nroot{ n }{ a } times nroot{ n }{ b }  = nroot{ n }{ a times b }
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nroot{ n }{ a } over { nroot{n}{b} } = nroot{ n }{ a over b }
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p nroot{ n }{ a } +- q nroot{ n }{ a } = ( p +- q ) nroot{ n }{ a }
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Example 3


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sqrt{ 54 } = sqrt{ 9 cdot 6 } = sqrt{ 9 } cdot sqrt{ 6 } = 3 sqrt{ 6 }
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sqrt{ 72 } = sqrt{ 36 cdot 6 } = sqrt{ 36 } cdot sqrt{ 2 } = 6 sqrt{ 2 }
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sqrt{ 2 over 25 } = sqrt{ 2 } over sqrt{ 25 } = sqrt{ 2 } over 5
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nroot{ 3 }{ 128 } = nroot{ 3 }{ 64 } = nroot{ 3 }{ 64 } cdot nroot{ 3 }{ 2 } = 4 nroot{ 3 }{ 2 }
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Example 4


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sqrt{ 45 } + 3 sqrt{ 20 } - 5 sqrt{ 5 } = 3 sqrt{ 5 } + 3( 2 sqrt{5} ) - 5 sqrt{ 5 }
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( 2 sqrt{3} + sqrt{2} )( 3 sqrt{3} - 5 sqrt{2} ) = 6 cdot 3 - 10 sqrt{ 6 } + 3 sqrt{ 6 } - 5 cdot 2
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Example 5


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sqrt{ x } = x^{ 1 over 2 }
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nroot{ 3 }{ 5 } = 5^{ 1 over 3 }
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nroot{ 4 }{ p^4 } = p^{ 3 over 4 }
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nroot{ 5 }{ a^10 } = a^{ 10 over 5 } = a^2
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Example 6


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( x^2 ){ 1 over 3 } = x{ 2 over 3 } = nroot{ 3 }{ x^2 }
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( 6p ){ 3 over 4 } = nroot{ 4 }{ (6p)^3 } = nroot{ 4 }{ 6^3 p^3 }
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3x^{ 2 over 5 }y^{ 3 over 5 } = 3 nroot{ 5 }{ x^2 y^3 }
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Example 7


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{ a }over{ sqrt{b} } = { a }over{ sqrt{b} } times {{ sqrt{b} }over{ sqrt{b} }} = a over b { sqrt{b} }
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3 over sqrt{ 6 } = 3 over sqrt{ 6 } times { {sqrt{6}}over{sqrt{6}} } = 3 over 6 { sqrt{6} } = 1 over 2 { sqrt{6} }
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Example 8


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a over { b + sqrt{c} } = a over { b + sqrt{c} } times { {b - sqrt{c}}over{b - sqrt{c}} } = a( b - sqrt{7} ) over { b^2 - c}
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a over { b - sqrt{c} } = a over { b - sqrt{c} } times { {b + sqrt{c}}over{b + sqrt{c}} } = a( b + sqrt{c} ) over { b^2 - c }
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Example 9


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sqrt{ 1 + x } = sum from{ n=0 } to{ infinity } {{ (-1)^n (2n)! }over{ (1-2n)(n!)^2(4^n) } x^n} = 1 + 1 over 2 { x } - 1 over 8 { x^2 } + 1 over 16 { x^3 } - 5 over 128 { x^4 } + ...,
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sqrt{ i } = 1 over 2 { sqrt{2} } + i { 1 over 2 }{ sqrt{2} } = sqrt{ 2 } over 2 { (1 + i) }
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i = cos( %pi over 2 ) + i sin( %pi over 2 )
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Example 10


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sqrt{ z } = sqrt{ r } e^{ i %ivarphi/2 } .
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sqrt{ r(cos %ivarphi + i sin %ivarphi)  } = sqrt{ r } [ cos %ivarphi over 2 + i sin {%ivarphi over 2} ]
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Download Sample Documents




Here are the document files containing all square root equations above for Math and Writer. These files are licensed under CC BY-SA 3.0 so you have the right to use, copy, study, edit, and share the files.

LibreOffice Math (.odf)
LibreOffice Writer (.odt)

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