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Call this number "x". In this case:x = root(5 root(5 root(5 root(5...

Since the expression inside the first root is equal to the entire expression, you get:

x = root(5 x)

Squaring both sides, to get rid of the rood, you get:

x squared = 5x

x squared - 5x = 0

x(x - 5) = 0

So, x is either equal to 0, or to 5. Indeed, if you start with any number and repeatedly multiply by 5 and then take the square root, you get closer and closer to 5... unless you start with zero, in which case you get exactly zero.

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