What is the square root of square root's square root?

Let the coefficient by 'x'

Hence

its square root is x^(1/2) or x^(0.5)

Then the square root again is [x^(1/2)]^(1/2)

Third time over {[x^(1/2)]^(1/2)}^(1/2)

Now the rules of indices are

[x^(n)[^(m) = x^(nm) When terms are 'nested' , multiply together.

Also

x^(n) X x^(m) = x^(n+m)

x^)n) / x^(m) = x^(n-m)

However, the first rule (nesting) applies in this case, when you multiply the indices together/

Hence x^(1/2 X 1/2 X 1/2) = x^(1/8) , Which is the 8th root.!!!!!