# Did anyone ever build a mechanical device to take fifth roots, or solve general quintics?

This question is from a post from John Baez's blog on, among other things, geometrical constructions. I was hoping someone here might know the answer.

In his post, Baez writes that

Nowadays we realize that if you only have a straightedge, you can only solve linear equations. Adding a compass to your toolkit lets you also take square roots, so you can solve quadratic equations. Adding neusis on top of that lets you take cube roots, which—together with the rest—lets you solve cubic equations. A fourth root is a square root of a square root, so you get those for free, and in fact you can even solve all quartic equations. But you can’t take fifth roots.

Puzzle 5. Did anyone ever build a mechanical gadget that lets you take fifth roots, or maybe even solve general quintics?

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Are electrons considered mechanical? :) –  Bruno Joyal Mar 29 '12 at 4:17
You can calculate 5th roots on a slide rule - does that qualify? –  Gerry Myerson Mar 29 '12 at 5:29
I'd be interested to see a mechanical device, which every time you push its pedal, it spits out one more decimal digit of $\sqrt{2}.$ –  user2468 Mar 29 '12 at 5:34

See also this paper and this short note on a machine by Leonardo Torres based on the so-called "endless spindle" mechanism for computing the quantity $\log(a+b)$ from $\log\,a$ and $\log\,b$.