Question

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?

Answer 1

It's not necessary. Just nice. Imagine adding fractions with roots on the denominators.

Answer 2

If you have them only on the numerator then it's easy to just find integer common denominators so that you can combine multiple fractions.

Answer 3

It's different in that it's ugly and similar in that you need to find common denominators.

Answer 4

That's assuming they're fractions. If they're not fractions then example:

2x^2 + 3x^2 = 5x^2 versus 2sqrt(2) + 3sqrt(2) = 5sqrt(2). Same rules.