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  "body": "\n## Summary\n\nA functional square root of a map $f$ is a map $g$ with $g(g(x)) = f(x)$ for all $x$.\nIt is the [[iterative root|27C6J3YNZY]] of order $2$, and it is often called a half-iterate of $f$.\nIt answers the question of what it means to apply $f$ half a time.\nFunctional square roots of the exponential function and of other simple maps have a long history in iteration theory.\n\n## Explanations\n\n### L1 human\n\nSquaring a number has an inverse question: which number squared gives the result?\nFor maps, the analogue of squaring is applying the map twice.\nA functional square root of $f$ is a map that, done twice, has the same effect as $f$ done once.\nFor $f(x) = x + 2$ one root is $g(x) = x + 1$; for $f(x) = 4x$ two roots are $2x$ and $-2x$.\n",
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