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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク nested radical ： ウィキペディア英語版 nested radical In algebra, a nested radical is a radical expression (one containing a square root sign, cube root sign, etc.) that contains (nests) another radical expression. Examples include :$\backslash sqrt,$ which arises in discussing the regular pentagon, and more complicated ones such as :$\backslash sqrt()\backslash \; \}.$ == Denesting nested radicals == Some nested radicals can be rewritten in a form that is not nested. For example, :$\backslash sqrt\backslash ,,$ :$\backslash sqrt+\backslash sqrt,$ :$\backslash sqrt()\; =\; \backslash frac\}\backslash \; \}\; =\; \backslash sqrt\backslash pm\backslash sqrt.$ Squaring both sides of this equation yields: :$a\backslash pm\; b\; \backslash sqrt\; =\; d\; +\; e\; \backslash pm\; 2\; \backslash sqrt.$ This can be solved by finding two numbers such that their sum is equal to ''a'' and their product is ''b2c/4'', or by equating coefficients of like terms—setting rational and irrational parts on both sides of the equation equal to each other. The solutions for ''e'' and ''d'' can be obtained by first equating the rational parts: :$a\; =\; d\; +\; e,$ which gives :$d\; =\; a\; -\; e,$ :$e\; =\; a\; -\; d.$ For the irrational parts note that :$b\backslash sqrt\; =\; 2\backslash sqrt,$ and squaring both sides yields :$b^2\; c\; =\; 4de.$ By plugging in ''a'' − ''d'' for ''e'' one obtains :$b^2\; c\; =\; 4(a-d)d\; =\; 4ad\; -\; 4d^2.$ Rearranging terms will give a quadratic equation which can be solved for ''d'' using the quadratic formula: :$4d^2\; -\; 4ad\; +\; b^2\; c\; =\; 0,$ :$d=\backslash frac.$ Since ''a'' = ''d+e'', the solution ''e'' is the algebraic conjugate of ''d''. If we set :$d=\backslash frac,$ then :$e=\backslash frac.$ However, this approach works for nested radicals of the form $\backslash sqrt$ if and only if $\backslash sqrt$ is a rational number, in which case the nested radical can be denested into a sum of surds. In some cases, higher-power radicals may be needed to denest the nested radical. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「nested radical」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.