On the denesting of nested square roots

• Eleftherios Gkioulekas ^[1]
  1. [1] University of Texas Rio Grande Valley

     University of Texas Rio Grande Valley

     Estados Unidos

     
• Localización: International journal of mathematical education in science and technology, ISSN 0020-739X, Vol. 48, Nº. 6, 2017, págs. 942-953
• Idioma: inglés
• DOI: 10.1080/0020739x.2017.1290831
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• Resumen

  • 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.