Dan's Thoughts Thinking somewhat carefully

(define (square x) (* x x))
(define (great-enough? guess newguess)
  (< (abs (- 1 (/ guess newguess))) 0.0001))
(define (improve guess x)
  (/ (+ (/ x (square guess)) (* 2 guess))
     3))
(define (cube-root guess x)
  (if (great-enough? guess (improve guess x))
    guess
    (cube-root (improve guess x) x)))