Drag the point A so that the length DA is the number whose square root you want. [br]The length of the vertical segment CD is its square root.
Call the number whose square root you want N.[br]How to do the construction with straightedge and compass or geometry software:[br]1. On a ray, mark off a distance 1 (BD), then a further distance DA=N.[br]2. Find the midpoint of BA, and make a circle whose diameter is BA.[br]3. Construct a perpendicular to BA at D. It intersects the circle at C.[br][br]The proof depends on several other ingredients. See the applets[br][url=http://ggbtu.be/m2766051]Triangles Inscribed in a Circle[/url][br][url=http://ggbtu.be/m2799345]Three Similar Right Triangles[/url][br][url=http://ggbtu.be/m2799345]The Geometric Mean[/url]