O Método das terminações características na identificação de números quadrados perfeitos

The main objective of this research is the creation of a new algebraic tool called the Characteristic Terminations Method, capable of assisting both the identification of perfect square numbers and the calculation of the approximations of its square roots, although this is not our greatest priority, due to the range of numerical and efficient methods that can be used for the most part. The work started from the study of the sequence of the square numbers, aiming at its proper characterization, since it is a second order arithmetic progression, including the determination of its Density that we will conclude to be null and necessary to justify the creation of the Method. Tasks that must be fulfilled, avoiding the thorny search for its decomposition into prime factors, taking into account the computational drawbacks directly associated as the divisions by consecutive prime numbers. There is a fundamental aspect to understanding the text as a whole: The fact that there is a great concern in directing the entire analysis to the discrete dimension of the problem, transporting the most relevant discussions to the set of positive integers. We will also explore the main methods at our disposal, supposedly capable of solving both mentioned problems with the desired precision, under specific conditions that ultimately compromise its effectiveness, for example the Tries and Errors, despite its undeniable potential pedagogical