On the denesting of nested square roots |
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Authors: | Eleftherios Gkioulekas |
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Affiliation: | 1. School of Mathematical and Statistical Sciences, University of Texas Rio Grande Valley, Edinburg, TX, USAdrlf@hushmail.com eleftherios.gkioulekas@utrgv.edu |
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Abstract: | We present the basic theory of denesting nested square roots, from an elementary point of view, suitable for lower level coursework. Necessary and sufficient conditions are given for direct denesting, where the nested expression is rewritten as a sum of square roots of rational numbers, and for indirect denesting, where the nested expression is rewritten as a sum of fourth-order roots of rational numbers. The theory is illustrated with several solved examples. |
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Keywords: | Denesting roots nested radicals algebra |
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