Conversation so far:
what must be the same about two radicals before they can be added
In order to be able to combine radical terms together, those terms have to have the same radical part.
what happens if a radical operation is positive
The result of a radical operation is positive if the number under the radical is positive.
what happens if a radical is negative
A negative number under the radical with an even index number produces an irrational number.
anything else about radicals besides positive and negative operations
To multiply or divide two radicals, the radicals must have the same index number.

Question: how about in equations
Self-contained rewrite: how are radicals in equations