# 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