As Rahul noted, the expression is of the form (a+b)² = a² + b² + 2ab.
Here, a = √(8 + √63) and b = √(8 - √63).
Step by step:
a² = [ √(8 + √63) ]² = 8 + √63.
b² = [ √(8 - √63) ]² = 8 - √63.
ab = √(8 + √63) * √(8 - √63) = √[ 8 + √63)(8 - √63) ] = √ (64 - 8√63 + 8√63 - 63) = √1 = 1.
Thus:
a² + b² + 2ab = (8 + √63) + (8 - √63) + 2*1 = 16 + 2 = 18.
The correct answer is C.
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