(define (square-roots myList)
  (if (null? myList) '()
      (cons (sqrt (car myList)) (square-roots (cdr myList)))))

Welcome to DrScheme, version 205. Language: Textual (MzScheme, includes R5RS).

> (square-roots '(1 2 3 4 100 200 500))
(1
 1.4142135623730951
 1.7320508075688772
 2
 10
 14.142135623730951
 22.360679774997898)

> (map sqrt '(2 4 6 8 100 625))
(1.4142135623730951 2 2.449489742783178 2.8284271247461903 10 25)

> (positives '(1 3 5 -22 44 0 -16 -8 444))
(1 3 5 44 444)

(define (positives myList)
  (cond ((null? myList) '())
        ((positive? (car myList)) (cons (car myList) (positives (cdr myList))))
        (else (positives (cdr myList)))))

> (square-roots (positives '(-1000 25 18 -16 1024 0)))
(5 4.242640687119285 32)

(define (atom? element)
  (not (list? element)))

(define (count-atoms myList)
  (cond ((null? myList) 0)
        ((atom? (car myList)) (+ 1 (count-atoms (cdr myList))))
        (else (+ (count-atoms (car myList)) (count-atoms (cdr myList))))))

> (list? '(3))
#t
> (list? '3)
#f
> (atom? '33)
#t

> (count-atoms '(1 2 3 (44 55 66) 7 88 (99 1010) ()))
10

> (define myList '(2 4 6 8 10 12 14))

> (list-tail myList 4)
(10 12 14)
> (list-tail myList 0)
(2 4 6 8 10 12 14)
> (list-tail myList 7)
()

> (list 33 55)
(33 55)
> (cons '(22 33) '(44 55 66 77))
((22 33) 44 55 66 77)

> (listify 123 '(222 333 444))
(123 222 333 444)

> (listify 123 555)
(123 555)

(define (listify element1 element2)
  ((if (list? element2) cons list) element1 element2))