If , then is:
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Thanks! I was stuck on this for a while. The key was realizing that since x is negative, |x| = -x, so -x|x| = -x(-x) = x^2. Then sqrt(x^2) = |x| = -x. Choice A.
Exactly! I initially forgot to take the absolute value after squaring, but since x is negative, |x| = -x. Glad it clicked.
Nice breakdown. I also got A after plugging in x = -2 to verify.
Wait, isn't the answer supposed to be positive? Since sqrt returns the principal square root, shouldn't it be positive? But -x is positive because x is negative. So A is positive. Makes sense.
Yes, exactly. The radical always gives a non-negative result, and -x is positive here. So no contradiction.
Is there a faster way to do this? I spent too long on it. Any tips for similar problems?
Just remember that sqrt(x^2) = |x|, and then use the sign of x to simplify |x|. That usually does it.
Also, plugging in a negative number like -3 can help you see the pattern quickly.
This was a bit challenging because I second-guessed myself on the absolute value. But after reviewing, it's clear. Good question!
What it tests
Your handling of square and higher roots, including simplifying radicals.
Common trap
Forgetting the ± when taking a square root to solve an equation, or assuming √(a²) = a.