Decide if radical expression equals a given rational number Given a radical expression an a rational number. Is there an algorithm to decide if the expression equals the number?
Example:
$(\sqrt{\sqrt[5]{74} - \sqrt[14]{78}})^{356}+\sqrt[6]{63} \overset{?}= 3$

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.
