@article {ChKaKaVa2005,
 author="A. Chigogidze, A. Karasev, K. Kawamura and V. Valov",
 title={On $C^{\ast }$-algebras with the approximate $n$-th root property},
 journal="Bull. Austral. Math. Soc.",
 fjournal={Bulletin of the Australian Mathematical Society},
 volume="72",
 year="2005",
 number="2",
 pages="197--212",
 issn="0004-9727",
 coden="ALNBAB",
 language="English",
 date="3rd March, 2005",
 classmath="46L85, 54C40",
 publisher={AMPAI, Australian Mathematical Society},
 MRnumber="MR2183403",
 ZBLnumber="02246384",
 url="http://www.austms.org.au/Publ/Bulletin/V72P2/722-5072-ChKaKaVa/index.shtml",
 acknowledgement={ The second author was partially supported by his NSERC Grant 257231-04. The paper was started during the third author's visit to Nipissing University in July 2004. The last author was partially supported by his NSERC Grant 261914-03.},
 abstract={ 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 $\varepsilon >0$ there exists $b\in X$ such that $\|b\|\leq 1$ and $\|a-b^n\|<\varepsilon $. 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 (respectively, commutative) separable unital \break $C^*$-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 {\v C}ech cohomology. }
}