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.

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Title: An Analytical Study of the Nested Radical Identity for sqrt(a ± b) and Its Applications in Algebraic Simplification
Grade: C
Author: Fazal Rehman (Author)
Publication Year: 2026
Pages: 4
Catalog Number: V1714534
ISBN (PDF): 9783389186770
Language: English
Tags: analytical study nested radical identity applications algebraic simplification
Product Safety: GRIN Publishing GmbH

Quote paper: Fazal Rehman (Author), 2026, An Analytical Study of the Nested Radical Identity for sqrt(a ± b) and Its Applications in Algebraic Simplification, Munich, GRIN Verlag, https://www.grin.com/document/1714534

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

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