Iterative Square Root

iterative_sqrt.scm

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

(define (sqrt x)
    (define (improve guess)
        (average guess (/ x guess)))

    (define (good-enough? guess)
        (< (abs (- (square guess) x)) (* 0.000001 x)))

    (define (sqrt-iter guess)
        (if (good-enough? guess)
              guess
              (sqrt-iter (improve guess)
        )
     ))
     
     (sqrt-iter 1.0)
)

(square (sqrt 9))               ; 3.000073824
(square (sqrt 0.0001))          ; 0.000100213
(square (sqrt 845000000000))    ; 845000004201