How about this?
3[√3+√5+√7]2 = 2[√3+√5+√7]2 + [√3+√5+√7]2
The original expression is now written as a sum of two terms. Can you finish the problem by showing that each of these terms is the square of something? I.e., can you identify A and B with the above being equal to A2 + B2?