Four Fours/Lemmata/Two Fours/64/Solutions

Puzzle: Two Fours: $64$

Using exactly $2$ instances of the number $4$, the task is to write an expression for $64$, using whatever arithmetical operations you consider necessary.

Solutions

Solution $1$

$64 = \paren {\sqrt 4}^{\map \Gamma 4}$

Solution $2$

$64 = \sqrt {\paren {\sqrt {\sqrt 4} }^{4!} }$

Solution $3$

$64 = 4^{\floor {\ln 4!} }$

Solution $4$

$64 = \map \phi {\map \phi {4^4} }$

Solution $5$

$64 = \paren {\map \phi {4!} }^\sqrt 4$

Solution $6$

$64 = 4^{\sqrt {\map {\pi} {4!} } }$