This question is from [a post from John Baez's blog](http://johncarlosbaez.wordpress.com/2012/03/15/tidbits-of-geometry/) on, among other things, geometrical constructions. I was hoping someone here might know the answer.

In his post, Baez writes that

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> 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.
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Which leads to the question:

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> **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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