Mechanisms for describing a square root function, from MIT

sqrt

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

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

(define (good-enough? guess x)
	(< (abs (- (square guess) x)) 0.001))

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

(define (sqrt x)
	(sqrt-iter 1.0 x))

// improvement, with proper block scoping	
(define (sqrt x)
	(define (good-enough? guess)
		(< (abs (- (square guess) x)) 0.001))
	(define (improve guess)
		(average guess (/ x guess)))
	(define (sqrt-iter guess)
		(if (good-enough? guess)
			guess
			(sqrt-iter (improve guess))))
	(sqrt-iter 1.0 x))