Root Repetition

When you put radical signs over each other, something cool happens to the number underneath them! Observe below:

The square root of a square root is the 4th root of a number, & the square root of that is the 8th root, & the square root of that is the 16th root, etc. As pictured above, another number can substitute for 2 on the radical signs, like 3 as in this example; the cube root of a cube root is the 9th root of a number, & the cube root of that is the 27th root, & the cube root of that is the 81st root, etc. It's exponential!

P.S.: If x = 0 or 1, then it doesn't matter what y is; however, there's no such thing as a zeroth(0th) root. 0 & 1 are the only 2 idempotent numbers.

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© Derek Cumberbatch