# 1.8

# SICP Exercise 1.8

Simply implementing Newton’s method of calculating cube roots.

```
(define (cube-iter guess x)
(if (good-enough? guess x)
guess
(cube-iter (improve guess x)
x)))
(define (improve y x)
(/ (+ (/ x (* y y)) (* 2 y)) 3))
(define (good-enough? guess x)
(< (abs (- (cube guess) x)) 0.0001))
(define (cube x) (* x x x))
(define (cbrt x)
(cube-iter 1.0 x))
```

Although this program suffers from the same issue we faced in SICP Exercise 1.7. That can be easily remedied by changing the good enough program procedure.

```
(define (good-enough? guess x)
(< (/ (cube guess) x) 0.0001))
```