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Quickest here is to let the whole thing be x and square it — the cross term collapses nicely into a difference of squares. Got 18 in about 30 seconds once I saw that.
Yeah, the nested radicals look scary but they cancel perfectly.
Took me a second to see why the middle term becomes 2*sqrt(64-63).
Is the trick just (a+b)^2 = a^2 + b^2 + 2ab and then the 2ab part simplifies? I keep trying to simplify each root separately and getting nowhere.
Don't simplify them individually, that's the trap. Square the sum first.
Think difference of squares under the outer root for the cross term.
Got 18. Medium difficulty — the setup is the whole question; after that it's just arithmetic.
What it tests
Your handling of square and higher roots, including simplifying radicals.
Common trap
Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.