I just came across a Wikipedia article [Nested Radicals](https://en.wikipedia.org/wiki/Nested_radical#Landau%27s_algorithm) that mentions [Landau's Algorithm](https://en.wikipedia.org/w/index.php?title=Landau%27s_algorithm&redirect=no) for deciding, whether a nested radical can be denested, but that Wikipedia article is just a stub.
Googling "Landau's Algorithms" produces references to the Wang and Landau Algorithm.



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> **Question:**
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> What role does Landau's Algorithm play in mathematical research, i.e. did it pave the way for further progress, e.g. towards a deterministic algorithm for denesting radicals, or did it "just" solve an isolated problem?
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> I am asking because [the original article](https://www.researchgate.net/publication/2629046_Simplification_of_Nested_Radicals) is freely accessible online, but isn't described in the omniscient Wikipedia.  
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> Is my impression right, that because Ramanujan provided some examples of denested radicals, that the topic is of some relevance?
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Relevance of Landau's Algorithm for Denesting Radicals
This 2017 article [Gkioulekas - On the denesting of nested square roots](https://www.researchgate.net/publication/314248287_On_the_denesting_of_nested_square_roots) summarizes the status of this topic. Landau's algorithm is not a "final" solution because it runs in exponential time with respect to the depth of the expression that one is attempting to denest. To find a general algorithm that runs in polynomial time remains an open problem. See also this related [MSE posting](https://math.stackexchange.com/a/4697/87355).


