Move blue T-bar to enter positive number x to be squared. Orange T-bar shows z = x^2
Move orange T-bar to enter positive number z to be rooted. Blue T-bar shows x = sqrt(z)
At point C there are 3 pink sliders (sliding in slots of violet, orange and blue bars respectively) connected together by revolution joints. The screw lead must be large enough to avoid self-locking.
The video shows operation 40^2 = 1600 or sqrt(1600) = 40 and then 70^2 = 4900 or sqrt(4900) = 70.
The mechanism works on similar triangles
آی-ویدئو