If √x+2=2, then (x+2)^2 equals

1981 AMC 12 Problem 1

Attempt Problem 1 of the 1981 AMC 12 below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 1981 AMC 12 solutions, or check the answer key.

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\sqrt{x+2}=2,

then

(x+2)^2

equals

\sqrt2

2

4

8

16

The equation already gives the value of

x+2

Square the known value once more

From

\sqrt{x+2}=2,

we get

x+2=4.

Therefore

(x+2)^2=4^2=16.

Therefore, the correct answer is E.