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# Super-root

In mathematics, the super-root is one of the two inverse functions of tetration. Just as exponentiation has two inverse functions: roots and logarithms, likewise tetration has two inverse functions: super-roots and super-logarithms. The super-root is the inverse function of tetration with respect to the base: if $^n y = x$, then "y" is an "n"th super root of "x".

Square root

The 2nd-order super-root, or "super square root", is noteworthy for its simple expression in terms of Lambert's W function. Namely,

:$ssqrt\left(x\right) = e^\left\{mathrm\left\{W\right\}\left(mathrm\left\{ln\right\}\left(x\right)\right)\right\}$

ee also

*Hyper operator

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