Finding intersection points of a circle with a line is equivalent to solving a system of equations, where one equation is that of a circle, (x-a)^2 + (y-b)^2 = r^2, and the second is that of a line, Ax + By = C. To solve it, you’ll be taking square roots, and not other roots. Similarly, to find intersection of two circles, you’ll be taking square roots, and not other roots.
Hypotenuse of a 1x2 unit right triangle, to be precise. By Pythagoras, the square root of any sum of squares can be drawn trivially with a compass and a straight edge. So 2, 5, 7, 10, 13, 17, etc