sqrt

Conformance: R5RS Scheme (Restrictions: Result is an integer. )

Purpose: Compute the square root of a natural number. (In fact, this function computes the greatest integer that is no greater than the square root of the given argument.)

Arguments:
X - square of root to extract

Implementation:

(define (sqrt square)
  (letrec
    ((_sqrt (lambda (x last)
       (cond ((= last x) x)
         ((= last (n+ 1 x))
           (if (n> (n* x x) square) (- x 1) x))
         (else (_sqrt (nquotient
                        (n+ x (nquotient square x))
                        2)
                      x))))))
    (cond ((negative? square)
        (bottom (list 'sqrt square)))
      (else (_sqrt square 0)))))

Example:

(sqrt 144) 
=> 12

See also:
digits, expt, gcd.