What is sqrt(7sqrt(7sqrt7)) ?

Khaleesi Herbert 2020-10-27 Answered
What is 777 ?
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pivonie8
Answered 2020-10-28 Author has 91 answers

Lets asume:
y=777,
y2=777,
y4=7277=737,
y8=767=77
So y=778=5.4886 . In general, if N is the number of 7's under the square root then y=7(2N)12N. In this case N=3 so y=723123=778. For N=4, y=71516=6.1984, as N approaches infinity y approaches 7. So for 7's repeated under square roots indefinitely the answer is 7.
Another way of solving it is to put y=7(7(7 So y2=77(77=7y, so since y0,y=7 (dividing through by y).

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