Consider terms built from elements of $\mathbb Q$ and the operations $+,\times,-,/$, and $\sqrt[n]{\,\cdot\,}$ for each natural number $n$. Given the promise that two terms are well-formed -- that is, there is no division by zero, and no even roots of negative numbers -- is there an algorithm which decides when the two terms are equal?A related question was posted here, but it is more general (as it allows arbitrary exponentiation, rather than just by rational numbers).
Decidability of Equality of Radical Expressions
computability;undecidability;number theory;equality