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 A^{2} + B^{2}?
