Advanced MathMediumSquare root of a perfect-square trinomial
Advanced Math practice question
For x > 0, which expression is equal to √(x² + 2x + 1)?
- A. x + 1Correct
- B. x − 1
- C. x + √(2x) + 1
- D. x² + 1
Answer: A. x + 1
x² + 2x + 1 = (x + 1)², and for x > 0 its square root is x + 1.
Why the other answers are wrong
- B. x − 1
- (x − 1)² = x² − 2x + 1, the wrong middle sign.
- C. x + √(2x) + 1
- A square root does not distribute over addition.
- D. x² + 1
- x² + 1 is not the square root of anything here; the root halves the degree.
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