Jenin Linear Algorithm (JLA): A Unified Mental Algorithm for Squares, Square Roots, and Cubes

This paper introduces the "Universal Squaring Method" (USM), an optimized mental arithmetic algorithm derived from the algebraic expansion of (10f + k)^2. By utilizing a "Full-Number Anchor" (n * f), the USM streamlines the cognitive process for squaring numbers of any magnitude, reducing the working memory load typically required for multi-step calculations.Additionally, the paper details the inverse application of the algorithm for rapid square root estimation. A comprehensive 50-point dataset is provided to verify the accuracy and efficiency of the method in both computational directions. This practitioner-led research offers a viable alternative to traditional mental math shortcuts for students and educators.