posted by Denay
Why is it important to simplify radical expressions before adding or subtracting? How is adding radical expressions similar to adding polynomial expressions? How is it different?
It is important to simplify radical expressions before adding/subtracting because there might be common factors in both numerator and denominator. You need to play around with terms, so you don't get complicated combined expression with same denominator!
When adding or subtracting radical expressions the rule says the radical must be the same before you combine the numbers out in front. To make the radical expressions the same you must first simplify them by factoring. Note that sometimes you can't make them the same so you leave the way it is.
It is important to simplify radical expressions before adding or subtracting to get terms with like radicals. Once we find terms with like radicals we can then add or subtract the expressions. Simplifying the expression and obtaining terms with like radicals makes the problem less complex when solving.