Question

In complete sentences explain why you can sometimes add square roots with different radicands. Give an example where you can add square roots with different radicands and an example where you cannot add square roots with different radicands.

Answer 1

Just as with "regular" numbers, square roots can be added together. But you might not be able to simplify the addition all the way down to one number. Just as "you can't add apples and oranges", so also you cannot combine "unlike" radical terms. In order to be able to combine radical terms together,

those terms have to have the same radical part.