Question

Why is it important to simplify radical expressions before adding or subtracting?

Answer 1

note that you cannot combine radical terms if their radicands (the terms inside the radical sign) are not equal.

for example,
sqrt(8) + sqrt(18)
you cannot add them right away since 8 is not equal to 18,, thus we first simplify each term.
for sqrt(8), note that we can rewrite it as
sqrt(2*2*2) = 2*sqrt(2)
for sqrt(18), note that we can rewrite it as
sqrt(2*3*3) = 3*sqrt(2)
since the radicands are equal, we can add them:
2*sqrt(2) + 3*sqrt(2) = 5*sqrt(2)

hope this helps~ :)