Geometric Construction of Square Roots via the Pythagorean Theorem

This GeoGebra example demonstrates how to construct a square root using a purely geometric setup based on the Pythagorean theorem. By building a right-angled triangle and enforcing c^2 = a^2 + b^2, it turns the algebraic act of taking a square root into locating a segment whose length corresponds to the desired √(·) value. Key concepts include the Pythagorean theorem, perpendicular (orthogonal) lines to create right angles, and the use of circles to transfer known lengths into new, computable distances. Construction workflow: Intersect is used to locate critical points from circle-line relationships; Circle and CircleArc provide circles with radii determined by given segments; Segment connects points to form the triangle sides; OrthogonalLine creates the right angle constraint; Angle and Polygon help define and keep the intended geometric configuration. The labeled points (e.g., a, b, A, B, C, …) represent the intermediate construction anchors, culminating in the segment that encodes the square root length. Suitable for secondary school geometry lessons, enrichment activities, and interactive demonstrations linking algebraic radicals to classical geometric construction.