You can put this solution on YOUR website! Whenever you add or subtract you must have like terms. The reason we simplify radicals first is that you won't know all the like terms until the radicals have been simplified.
Here's an example:
The first and last terms are like terms. We could subtract them now if we want:
The remaining terms are not like terms (yet). But we can simplify the first square root:
Now that the square roots are simplified we can see that the remaining terms are now like terms which we can add:
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