SOLUTION: is the suare root of x^2 = x an identity (true for all values of x) explain?

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Question 72584: is the suare root of x^2 = x an identity (true for all values of x) explain?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
No it is not, well maybe if you were more precise and said
sqrt%28x%5E2%29=abs%28x%29is an identity, you would be right(The bars show absolute value)
The simple reason why (there are more complicated versions which have their purpose) is because when you take the square root of any number you get 2 answers. For instance
sqrt%284%29 equals plus or minus 2 (we need to have both). Since the absolute value of both a positive and a negative number is positive, the absolute value can be used in this case.
abs%28x%29=a
x=0%2B-aThis is why abs%28x%29 is used in the identity instead of x (ignore the 0).