My solution to exercise 1.8 from Structure and Interpretation of Computer Programs

sicp_ex1-8.scm

#lang scheme
(define (cube-root x)
  (define (approx guess x)
    (if (good-enough? guess x)
      guess
      (approx (improve guess x) x)))
  (define (improve guess x)
    (/ (+ (/ x (square guess)) (* 2 guess)) 3))
  (define (good-enough? guess x)
    (< (abs (- (cube guess) x)) 0.001))
  (define (square x)
    (* x x))
  (define (cube x)
    (* (square x) x))
  (define (abs x)
    (if (< x 0) (- x)
      x))
  (approx 1.0 x))