Advanced MathHardSquare root of a perfect square with a negative variable
Advanced Math practice question
If x < 0, which expression is equal to √(9x²)?
- A. −3xCorrect
- B. 3x
- C. 3x²
- D. 9x
Answer: A. −3x
√(9x²) = 3|x|. For x < 0, |x| = −x, so the value is −3x (a positive number).
Why the other answers are wrong
- B. 3x
- 3x is negative when x < 0, but a square root is never negative.
- C. 3x²
- 3x² has the wrong degree; the square root halves the exponent.
- D. 9x
- 9x forgets to take the square root of 9.
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