Four Fours/64

Puzzle

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

Solutions

Solution $1$

$64 = \paren {4 + 4} \times \paren {4 + 4}$

Solution $2$

$64 = \dfrac {4! + .4 \times 4} {.4}$

Solution $3$

$64 = \dfrac {4!} {.4} + \sqrt 4 + \sqrt 4$

Solution $4$

$64 = 4 \times 4 \times \sqrt 4 \times \sqrt 4$

Solution $5$

$64 = 4 \uparrow {\paren {4 - \dfrac 4 4} }$

Solution $6$

$64 = \sqrt 4 \uparrow {\paren {\sqrt 4 + \sqrt 4 + \sqrt 4} }$

Solution $7$

$64 = \paren {4 + 4} \uparrow \paren {4 - \sqrt 4}$

Also see

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