Geometric demonstration of integer square roots via construction

This GeoGebra example illustrates the idea of integer square roots by building a geometric construction that lets learners visually test and connect “squaring” with “integer roots.” The main math concepts are the integer–square relationship (for integers n, if n = a^2 then √n = a is an integer) and how such conditions can be explored through interactive geometry and function-style checking. Construction-wise, it uses Random to select/generate values, Corner and Polygon to form the key geometric setup, Function to define the computational relationship used for verification, and Textfield to support user input and on-screen feedback. The workflow includes tracking results (e.g., right/wrong counts) and displaying the final outcomes along with the constructed objects. Suitable for middle/high school and early undergraduate learners for visual number theory practice, quadratic relationship reasoning, and geometry–function integration.