#### 15.5.2 Nth Root

Integer Nth roots are taken using Newton’s method with the following
iteration, where *A* is the input and *n* is the root to be taken.

1 A
a[i+1] = - * ( --------- + (n-1)*a[i] )
n a[i]^(n-1)

The initial approximation *a[1]* is generated bitwise by successively
powering a trial root with or without new 1 bits, aiming to be just above the
true root. The iteration converges quadratically when started from a good
approximation. When *n* is large more initial bits are needed to get
good convergence. The current implementation is not particularly well
optimized.