Represent 4 with four identical digits using only the usual arithmetic operations, factorials and square roots

Solution

1 + 1 + 1 + 1 = 4
2×2 + 2 - 2 = 4
√3×√3 + 3/3 = 4
√4×√4 + 4 - 4 = 4
5 - √5×√5/5 = 4
6 - (6 + 6)/6 = 4
77/7 - 7 = 4
√√(8 + 8) + √√(8 + 8)= 4
√√9×√√9 + 9/9 = 4
0! + 0! + 0! + 0! = 4


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