TITLE: How to construct geometrically $\sqrt[k]{n}$ for $k \in \mathbb{Z}$ and $k>2$
QUESTION [8 upvotes]: As we know that square root of a number $n$ can be found by using a compass and a straight edge, given the line of length $n$.
What I want to know is how to find cube root, fourth root, fifth root or any $n$-th root of a number, by using any tools?
Few days ago I learned that origami (an art of folding paper) can be used as a tool to find cube root and even roots of a cubic equation. So I'm wondering about how to find any other $n$-th roots.
How to decide which kind of tools are necessary for the above mentioned operations? Thanks!

REPLY [3 votes]: Its seems that there are many extended constructions for the 3-th (cubic) root of two, for example this one based on J. H. Conway and R. K. Guy, The Book of Numbers, New York: Copernicus Books/Springer, 2006 pp. 194–195.:
Demonstration shows a construction of $\sqrt[3]{2}$ using a ruler with two marks
http://demonstrations.wolfram.com/ConstructingTheCubeRootOfTwo/
Using marked ruler is called neusis construction. It is more powerful than a conic drawing tool. But there are also negative results, and it is still open as to whether a regular 25-gon or 31-gon is constructible using this tool.