Amirkabir University of Technology AUT Journal of Mathematics and Computing 2783-2449 7 3 2026 07 01 Computing the matrix square root: A problem-solving approach using Mathematica and Pólya's strategies 303 320 5686 10.22060/ajmc.2025.23508.1262 EN Mandana Moccari Department of Mathematics, Ha. C., Islamic Azad University, Hamedan, Iran Journal Article 2024 09 05 This paper introduces a novel method for solving the matrix equation $X^2 - A = 0$ by computing matrix square roots. Inspired by George Pólya's structured problem-solving strategies and leveraging Wolfram Mathematica, the approach offers a systematic, efficient, and clear solution to the problem. The method extends the computation of matrix square roots to large matrices and those with complex eigenvalues, significantly broadening its applicability in diverse fields, including control theory, quantum physics, and signal processing. The approach is demonstrated through comprehensive examples and original Mathematica code, providing a practical toolkit for solving similar mathematical challenges. The method is designed to be both intuitive and versatile, making it a valuable resource for educators, students, and researchers engaged in advanced mathematical problem-solving. https://ajmc.aut.ac.ir/article_5686_07bb5fdef1ee99d35eaccce14f8b5540.pdf