Four Fours/23

Puzzle

Using exactly $4$ instances of the number $4$, the task is to write an expression for $23$, using whatever arithmetical operations you consider necessary.

Solutions

Solution $1$

$23 = 4! - 4 + \sqrt {\dfrac 4 {. \dot 4} }$

Solution $2$

$23 = \dfrac {4! \times 4 - 4} 4$

Solution $3$

$23 = 4! - \dfrac {\sqrt 4 + \sqrt 4} 4$

Also see

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