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Question: sqrt(x^2)

Question:sqrt(x^2)

GeorgeJ 1090 Maple
February 15 2007
0
If you ask most people "what is the square root of 64?" they will answer "8". Of course we know that the technically correct answer is {8,-8}. So I'm a bit confused that when I ask MAPLE to simplify sqrt(x^2) it spits the expression right back to me, but when I tell MAPLE to give me sqrt(x^2) assuming x>0 it gives me x. It seems to me that there are going to be two answers whether or not x>0. That is, the answer to sqrt(x^2) is {x,-x} whether or not x>0. That is, sqrt((-8)^2) = sqrt(8^2) = {8,-8}. So when I am using symbols rather than numbers why does MAPLE give me the answer x for sqrt(x^2) assuming x>0, but give me the answer sqrt(x^2) when I don't include the assumption?
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