Question

Solve
Root(18+2root65) + root(36+2 root15)=?

Answer 1

look at the 2√65 of the first term. 65 = 13*5 , mmmhhhh?
consider (√5 + √13)^2 = 5 + 2√65 + 13 = 18 + 2√65

then √(18+2√15) = √[(√5 + √13)^2] = √5 + √13

in the same way:
(√5 + √3)^2 = 5 + 2√15 + 3 = 8 + 2√15
oops
was expecting 36 + 2√15
since 15 can only be factored to 3*5, I am unable to express
√(36+2√15) as separate radicals

check to make sure you didn't have a typo.

In these kind of questions, usually there would be another √5 or √13
popping up from the second term, so that they can be added.