**Q:** Newton's method for cube roots is based on the fact that if y is an approximation to the cube root of x, then a better approximation is given by the value:

Use this formula to implement a cube-root procedure analogous to the square-root procedure. (In section 1.3.4 we will see how to implement Newton's method in general as an abstraction of these square-root and cube-root procedures.)

**A:**

```
;; The setup is the same, except for the names.
(define (cbrt-iter guess x)
(if (good-enough? guess x)
guess
(cbrt-iter (improve guess x)
x)))
(define (cube x)
(* x x x))
(define (good-enough? guess x)
(< (abs (- (cube guess) x)) 0.001))
(define (cbrt x)
(cbrt-iter 1.0 x))
;; The formula in scheme.
(define (improve guess x)
(/
(+ (/ x (* guess guess)) (* 2 guess))
3))
;; A few guesses.
(display (cbrt 8))
(newline)
(display (cbrt 27))
(newline)
(display (cbrt 60))
(newline)
```

```
2.0000049116755
3.00000054106418
3.91487458417134 ; My calculator gives 3.91486764117
```