To achieve the number 77 with four fours, the solution is as follows:
sqrt(4/.4)4 - 4
Instead of the second four being equal to four tenths, place a dot over the top to indicate it being equal to four ninths.
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There are 77 eighty-fours in 672
[√(4/.4*)]^4 - 4 = [√9]^4 - 4 = 3^4 - 4 = 81 - 4 = 77 N.B. the denominator within the square root is meant to be 0.4 recurring, which is written with a dot above the 4 but I am not able to do this. 0.44444...... = 4/9 Also, if you do (4-40)3 - 4
A solution to the four fours problem for the number 33 is: 33 = (4-.4)/.4+4!
The only solution that I have ever seen uses some notation that is not so commonly used, namely a bar over 4 to mean the infinitely repeating decimal .44444... which is 4/9 . So, if x = 4/9 is written with one four, then sqrt(4/x) 4 - 4 uses four fours and equals 77 since 4/x = 4 * 9/4 = 9 and sqrt(9)4 - 4 = 34 - 4 = 81 - 4 = 77.
(4x4) - (4/4)