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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 Square root of 5 ： ウィキペディア英語版 Square root of 5 }}} |} The square root of 5 is the positive real number that, when multiplied by itself, gives the prime number 5. It is more precisely called the principal square root of 5, to distinguish it from the negative number with the same property. This number appears in the fractional expression for the golden ratio. It can be denoted in surd form as: :$\backslash sqrt.\; \backslash ,$ It is an irrational algebraic number.〔Dauben, Joseph W. (June 1983) Scientific American ''Georg Cantor and the origins of transfinite set theory.'' Volume 248; Page 122.〕 The first sixty significant digits of its decimal expansion are: :2.23606 79774 99789 69640 91736 68731 27623 54406 18359 61152 57242 7089... . which can be rounded down to 2.236 to within 99.99% accuracy. As of December 2013, its numerical value in decimal has been computed to at least ten billion digits.〔Lukasz Komsta: ''(Computations page )''〕 ==Proof of irrationality== This irrationality proof for the square root of 5 uses Fermat's method of infinite descent: Suppose that √5 is rational, and express it in lowest possible terms (i.e., as a fully reduced fraction) as $\backslash frac$ for natural numbers ''m'' and ''n''. Then √5 can be expressed in lower terms as $\backslash frac$, which is a contradiction.〔Grant, Mike, and Perella, Malcolm, "Descending to the irrational", ''Mathematical Gazette'' 83, July 1999, pp.263-267.〕 (The two fractional expressions are equal because equating them, cross-multiplying, and canceling like additive terms gives $5n^2=m^2$ and $\backslash tfrac=\backslash sqrt$, which is true by the premise. The second fractional expression for √5 is in lower terms since, comparing denominators, 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「Square root of 5」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.