  We say that a C*-algebra X has the approximate n-th root property (n\geq 2)
if for every a\in X with ||a||\leq 1 and every \epsilon>0 there exits b\in X
such that ||b||\leq 1 and ||a-b^n||<\epsilon. Some properties of commutative
and non-commutative C*-algebras having the approximate n-th root property are
investigated. In particular, it is shown that there exists a non-commutative
(resp., commutative) separable unital C*-algebra X such that any other
(commutative) separable unital C*-algebra is a quotient of X. Also we
illustrate a commutative C*-algebra, each element of which has a square root
such that its maximal ideal space has infinitely generated first Cech
cohomology.
