Hi Ami,
I'm happy to help. Here's how the math "works."
(X + Y)^2 = X^2 + 2XY + Y^2
X =√(8 + √63)
Y =√(8 - √63)
There are 3 terms that we have to figure out. The two squared-terms are actually pretty fast though, since "squaring a square-root" cancels out the two math functions....
X^2 = (√(8 + √63))^2 = 8 + √63
Y^2 = (√(8 - √63))^2 = 8 - √63
The "middle term" will take a little bit of extra work, since we have to FOIL out these terms:
2XY = 2(√(8 + √63))(√(8 - √63))
= 2(√[64 + 8√63 - 8√63 - 63]) = 2(√1) = 2
In the end, we have 8 + √63 + 2 + 8 - √63
The two squared terms cancel out and we're left with:
8 + 2 + 8 = 18
Final Answer:
GMAT assassins aren't born, they're made,
Rich