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Jim
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Is there an algorithm for determining whether an expression involving nested radicals is rational?

Specifically, consider expressions involving integers, addition, multiplication, division, and nth roots for any positive integer n. Is there an algorithm that can determine whether such an expression is a rational number? If the expression is a rational number, is it possible to determine which rational number (e.g. test whether an expression is 0?

I've seen papers on denesting radicals, but I couldn't find anything on testing for rationality.

Jim
  • 301
  • 3
  • 3