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An Analytical Study of the Nested Radical Identity for sqrt(a ± b) and Its Applications in Algebraic Simplification

Titel: An Analytical Study of the Nested Radical Identity for sqrt(a ± b) and Its Applications in Algebraic Simplification

Wissenschaftlicher Aufsatz , 2026 , 4 Seiten , Note: C

Autor:in: Fazal Rehman (Autor:in)

Mathematik - Allgemeines, Grundlagen

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This article examines the nested radical identity sqrt(a ± b) = sqrt( (a + sqrt(a^2 - b^2)) / 2 ) ± sqrt( (a - sqrt(a^2 - b^2)) / 2 ). We analyze its mathematical foundation, conditions of validity, and applications in simplifying complex radical expressions. The identity proves useful in algebra, number theory, and computational mathematics for denesting radicals and enhancing computational efficiency. Numerical verification through Python code confirms exact equivalence within floating-point precision.

Details

Titel
An Analytical Study of the Nested Radical Identity for sqrt(a ± b) and Its Applications in Algebraic Simplification
Note
C
Autor
Erscheinungsjahr
2026
Seiten
4
Katalognummer
V1714534
ISBN (eBook)
9783389186770
Sprache
Englisch
Schlagworte
analytical study nested radical identity applications algebraic simplification
Produktsicherheit
GRIN Publishing GmbH
Arbeit zitieren
Fazal Rehman (Autor:in), 2026, An Analytical Study of the Nested Radical Identity for sqrt(a ± b) and Its Applications in Algebraic Simplification, München, GRIN Verlag, https://www.hausarbeiten.de/document/1714534