A Digit-Based Algorithm for Computing Square Roots of Perfect Squares
DOI:
https://doi.org/10.5433/1679-0375.2026.v47.54706Keywords:
quare root algorithms, perfect squares, digit patterns, arithmetic progression, asymptotic complexityAbstract
This paper presents a new method for computing square roots of perfect squares, originally devised by two students from Basic Education during their mathematics studies. Motivated by numerical patterns observed in the decimal representation of perfect squares, the method combines classical properties of unit digits with a novel block-based structure derived from arithmetic progressions. These patterns allow the construction of an explicit algorithm that recovers the square root of a perfect square using only elementary operations. The work provides a rigorous mathematical formalization of the method, including proofs of correctness, an analysis of its asymptotic behavior, and a discussion of its computational complexity. Beyond its theoretical interest, the proposed approach highlights the mathematical creativity of young students and illustrates how elementary observations can lead to meaningful mathematical structures, reinforcing connections between school mathematics, undergraduate research, and outreach activities.
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Copyright (c) 2026 João Alexandre Zambaldi Garcia, Felipe Kenji Iokota, Paulo Liboni, Luís Rafael Carvalho Moreira, Pablo Marcelo Arboleya Nogueira, Eduardo Henrique de Santana, Fabrício Ventura da Silva
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