Given a radical expression an a rational number. Is there an algorithm to decide if the expression equals the number?
Example:
$(\sqrt{\sqrt[5]{74} - \sqrt[14]{78}})^{356}+\sqrt[6]{63} \overset{?}= 3$
2026-03-25 09:23:20.1774430600
Decide if radical expression equals a given rational number
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An expression that involves the operations addition, multiplication, root extraction (and NOT DIVISION) with natural numbers will yield an algebraic integer. You claim that number is a rational number so it has to be an integer. So if the number is approximately 3 then it will be exactly 3.
You have to find the approximate value with control on errors using calculators, or numerical methods.