sicp-1.8 created by dcb9 - https://repl.it/KVqC/7

sicp-1.8.sc

(define (square x) (* x x))
(define (double x) (+ x x))
(define (athird x) (/ x 3))
(define (cube x) (* x x x))
(define (abs x) (if (< x 0) (- 0 x) x))

(define (good-enough? guess x)
  (< (abs (- (cube guess) x)) 0.0000001))

(define (improve guess x) 
  (athird (+ (/ x (square guess)) (double guess))))

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

(define (cbrt x)
  (cbrt-iter 1.0 x))

(cbrt 9)
; (cbrt 64)
; (cbrt 27)