SOLUTION: Is sqrt x^2=x an identity (true for all values of x)? Answer: Explain your answer in this space.

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Question 73010: Is sqrt x^2=x an identity (true for all values of x)?
Answer:
Explain your answer in this space.

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, lets say you have
x%5E2=a
We cannot say the x=sqrt%28a%29 is true since there are two answers. This is the true answer
x=0%2B-sqrt%28a%29Since there are 2 answers (ignore the zero)


The same idea applies in this case; however, instead of using the plus or minus, we go for the absolute value since it represents the distance positive and negative numbers are from zero on the number line. In other words, since
abs%28x%29=a
x=0%2B-a (in other words, x is both positive and negative)
0%2B-sqrt%28x%5E2%29=xNow we can from this
sqrt%28x%5E2%29=abs%28x%29To this, which is an identity.
Hope that makes sense. Feel free to ask questions if you are lost.