Call the number whose square root you want N. How to do the construction with straightedge and compass or geometry software: 1. On a ray, mark off a distance 1 (BD), then a further distance DA=N. 2. Find the midpoint of BA, and make a circle whose diameter is BA. 3. Construct a perpendicular to BA at D. It intersects the circle at C. The proof depends on several other ingredients. See the applets Triangles Inscribed in a Circle