;; root : Number Number -> Number
; generalized form of sqrt* function; finds the root of given number
;(check-expect (root 9 2) 3) approximatelly
;(check-expect (root 0 123) 0) approximatelly
;(check-expect (root -1 2) 0+1i) approximatelly
;(check-expect (root -4 2) 0+2i) approximatelly
(define (root n m)
  (root-iter 1.0 n m))

; root-iter: Number Number Number _> number
; consumes guess, x, y where resulting value is equal to x^1/y
; cannot provide examples
(define (root-iter guess n m)
  (if (root-good-enough? guess n m)
      guess
      (root-iter (root-improve guess n m) n m)))

;root-good-enough?: number number number -> number
;checks whether given guess is near the given x by 0.001 much
(define (root-good-enough? guess n m)
   (< (abs (- n (expt guess m))) 0.001))

;root-improve: number number -> number
(define (root-improve guess n m)
  (/ (+ guess (/ n (expt guess (- m 1)))) 2))


(define (getridoffraction x) (/ 1000000000 (round (* 1000000000 x))))