Answer: If you have a segment AB, place the unit length segment on the line where AB lies, starting with A and in the direction opposite to B; let C be the other point of the segment. Now draw a semicircle with diameter CB; and a line perpendicular to A; this line crosses the semicircle in a point D. AD is then the square root of AB.
△BCD is a right triangle, like △ACD and △ABD; all of these are similar, so you find out that AC/AD=AD/AB. But AC=1, so AD=√AB.
Step-by-step explanation: See the drawing below: