(define (new-if predicate then-clause else-clause)
  (cond (predicate then-clause)
        (else else-clause)))

(define (square x) (* x x))

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

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

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

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

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

(sqrt 9)
;3.00009155413138
(sqrt (+ 100 37))
;11.704699917758145
(sqrt (+ (sqrt 2) (sqrt 3)))
;1.7739279023207892
(square (sqrt 1000))
;1000.000369924366

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