Simplification of Square Roots and Prime Factorization

This applet demonstrates the simplification of square roots through prime factorization in GeoGebra. It combines the Sequence, Product, and Factors commands to automatically compute the prime factorization of a given number and extract perfect-square factors out from under the radical sign, rewriting the expression in its simplest form. The tool walks students through each step of the algebraic process: first decomposing the radicand into its prime factors, then grouping factors into pairs, identifying the perfect squares, and finally pulling the square roots of those perfect squares outside the radical while leaving any unpaired prime factors inside. The applet provides an interactive, visual representation of a procedure that many middle school and high school algebra students find challenging. By animating the step-by-step simplification, it helps learners see exactly how prime factorization connects to radical reduction, reinforcing the relationship between these two core algebra topics. Students can input different numbers and immediately observe how the factors reorganize and which terms move outside the root, building both procedural fluency and conceptual understanding. This resource is designed for classroom instruction at the secondary algebra level. Teachers can use it as a demonstration tool during lessons on radicals, as a self-guided practice activity for independent or small-group work, or as a homework support resource that allows students to check their own simplification steps. The clear visual breakdown of each transformation reduces cognitive load and gives learners confidence in their ability to handle more complex radical expressions, including those involving variables.