I am a Math 7/8 teacher. I was wondering how you would show a student how to find the exact location of the square root of three on the number line using just a compass and a straight edge.
One way you can do this is to use the Theorem of Pythagoras. Draw a line. At a point A on the line construct a line which is perpendicular to the first line. Mark a point C on this line a distance of one unit from A.
Now you have a right triangle with hypotenuse of length 2 units and one side of length 1 unit. Hence, by Pythagoras' Theorem