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Evaluate sqrt(3 + sqrt(3) + sqrt(2 + sqrt(3) + sqrt(7 + sqrt(48)))).

1. 1 + sqrt(3)
2. 2 + sqrt(3)
3. sqrt(3)
4. 3

Correct answer: 1 + sqrt(3)

Solution

Each layer simplifies to a perfect square of the form (a + b*sqrt(3))², collapsing the nested radicals one by one.

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