Is there some way to determine how many times one must root a number and its subsequent roots until it is equal to the square root of two or of the root of a number less than two?
sqrt(16)=4
sqrt(4)=2
sqrt(2) ... 3
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sqrt(27)=5.19615...
sqrt(5.19615...)=2.27950...
sqrt(2.27950...)=1.509803...
sqrt(1.509803...) ... 4
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Also, using the floor function...
sqrt(27)=floor(5.19615...)
sqrt(5)=floor(2.23606...)
sqrt(2) ... 3