If √2+√x=3, then x=

1995 AMC 12 Problem 2

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\sqrt{2+\sqrt{x}}=3,

then

x=

1

\sqrt7

7

49

121

Square both sides once to isolate

\sqrt{x}

After isolating the inner radical, square a second time

Squaring gives

2+\sqrt{x}=9,

\sqrt{x}=7.

Squaring again gives

x=49.

Thus the correct answer is D.