To combine radicals using addition or subtraction, the radicals must be like terms, meaning they must have the same radicand (the expression inside the radical) and the same index of the root. For example, \(\sqrt{2} + \sqrt{2} = 2\sqrt{2}\), but \(\sqrt{2} + \sqrt{3}\) cannot be combined because the radicands are different.
It cannot always be immediately determined whether radicals can be combined because the expressions under the radical signs may not be straightforward to compare. For instance, when dealing with variables or more complex expressions, one may need to simplify them first to check if they can be expressed in a form that reveals whether they are like terms. Additionally, the radicals could be expressed in different forms, such as \(\sqrt{4} = 2\) and \(\sqrt{16} = 4\), where understanding equivalence requires simplification. Therefore, careful analysis and sometimes algebraic manipulation are often necessary to determine if combination through addition or subtraction is possible.
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