Constructible number, now a Good Article on Wikipedia: https://en.wikipedia.org/wiki/Constructible_number
This concerns the correspondence between compass-and-straightedge constructions and formulas using square roots, and the use of that correspondence to prove the impossibility of classical geometric construction problems. Relatedly, see Joel Hamkins' new blog post http://jdh.hamkins.org/the-hierarchy-of-geometric-constructibility-can-we-go-back/ on how constructibility of one set of points from another produces an equivalence relation on pairs of points.
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