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? Provide a radical expression for your classmates to simplify.

Answer 1

Why is it important to simplify radical expressions before adding or subtracting?
You have to simplify radical expressions before adding or subtracting because you can only add or subtract expressions with the same value inside the radical sign.
How is adding radical expressions similar to adding polynomial expressions? How is it different?
It is similar to adding polynomials because in polynomials you can also only add or subtract terms if they are like terms (variables with the same powers). In radical expressions, you can also only add or subtract like terms (the same value inside the radical). One main difference is that in polynomials, like terms are determined by the variables and their powers, while in radical expressions, like terms are determined by the value inside the root.
Provide a radical expression for your classmates to simplify.
Consider participating in the discussion by simplifying your classmates' expressions. Detail what would have happened or if the expression was not simplified first.
Here is an example for the classmates:
sqrt(180) - sqrt(20)
Factor the 180 and 20:
sqrt(5*36) - sqrt(5*4)
Simplify:
6 * sqrt(5) - 2 * sqrt(5)
Subtract:
4 * sqrt(5)
If you did not simplify this expression first, you would end up with the wrong answer.

Answer 2

answer this problemSQRT (18) + SQRT (72).