#| BEGIN (Write your solution here) |#
(define (square x) (* x x))

(define (cube x) (* x x x))

(define (cube-root x)
  (cube-root-iter 1.0 x))

(define (cube-root-iter guess x)
  (if (good-enough? guess x)
      guess
      (cube-root-iter (improve guess x) x)))

(define (improve guess x)
  (/ (+ (/ x (square guess)) (* 2 guess)) 3))

(define (average x y)
  (/ (+ x y) 2))

(define (good-enough? guess x)
  (< (abs (- (cube guess) x))
     (* 0.0000001 guess)))
#| END |#