Four Fours/4

Puzzle

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

Solutions

Solution $1$

$4 = 4 - 4 + \sqrt 4 + \sqrt 4$

Solution $2$

$4 = \sqrt {4 + 4 + 4 + 4}$

Solution $3$

$4 = \sqrt {\dfrac 4 {.\dot 4} } + \dfrac 4 4$

where $.\dot 4$ is interpreted as $0.44444 \ldots = \dfrac 4 9$

Solution $4$

$4 = 4 + 4 - \sqrt 4 - \sqrt 4$

Solution $5$

$4 = \dfrac {4 \times 4} {\sqrt 4 + \sqrt 4}$

Solution $6$

$4 = \dfrac 4 {\sqrt 4} + \dfrac 4 {\sqrt 4}$

Also see

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