When adding radicals, do you add two radicands together even if they're different?

Question

How would you answer this equation in radical simplest form?
3 rad 12 + 3 rad 12 + 5 rad 8 +5 rad 8
I got 6 rad 12 + 25 rad 8
Is this right? Sorry if my questions are confusing, this is hard to explain.

Answer 1

3√12 + 3√12 + 5√8 + 5√8
= 6√12 + 10√8

but √12 = √4√3 = 2√3
and √8 = √4√2 = 2√2

so 6√12 + 10√8
= 6(2√3) + 10(2√2)
= 12√3 + 20√2

(We can only add/subtract "like" radicals, but we can multiply/divide them in this way ...
e.g. √5x√7 = √35 , √60 ÷ √2 = √30 )

Answer 2

Thanks, now I remember the teacher quickly rushing through that in class. ;)

Answer 3

Calamity , if mathematics should ever be rushed ....