Part 1: Explain, in complete sentences, how you might show that radicals should be simplified before being added or subtracted to another radical. (2 points)

Part 2: Give an example of an addition or subtraction problem of radicals where this would apply. (2 points)

please help !!!

Question

Part 1: Explain, in complete sentences, how you might show that radicals should be simplified before being added or subtracted to another radical. (2 points) 

Part 2: Give an example of an addition or subtraction problem of radicals where this would apply. (2 points)

please help !!!

anonymous · Answer

Radicals with the same radicands are added by adding their coefficients.
Example: 2sqrt3 +5sqrt3 = 7sqrt3
Sometimes the radicands are not equal before simplification, but are equal after simplification: 3sqrt8 +7sqrt18 = 6sqrt2 +21sqrt2 = 27sqrt2.

Multiplying by the conjugate eliminates the radical (or i).
(3-sqrt2)(3+sqrt2) = 9-2 = 7
(3-2i)(3+2i) = 9-4i^2 = 9+4 = 13