# Thread: absolute value

1. ## absolute value

Hello, some confusion here. Is sqrt(x^2) the same as (sqrt(x))^2. This is what I think: I know the first is the definition of the absolute value function. I think the second is different because it needs a positive domain. Also, if you solve the first you get 2 answers, one + and one -. The second only has positive answers. Is this correct?
thanks
bill

2. Originally Posted by billq
Is sqrt(x^2) the same as (sqrt(x))^2. This is what I think: I know the first is the definition of the absolute value function. I think the second is different because it needs a positive domain. Also, if you solve the first you get 2 answers, one + and one -. The second only has positive answers.
I agree with your comment is blue above. That is correct.
But do not agree with the part in red.
Where are the equations that go with solutions?
Both $\displaystyle \sqrt{2^2}~\&~\left(\sqrt2\right)^2$ have only one value $\displaystyle 2$.

However, $\displaystyle \sqrt{x^2}=2$ has two solutions.
Whereas, $\displaystyle \left(\sqrt{x}\right)^2=2$ has only one solution.

3. Originally Posted by Plato
I agree with your comment is blue above. That is correct.
But do not agree with the part in red.
Where are the equations that go with solutions?
Both $\displaystyle \sqrt{2^2}~\&~\left(\sqrt2\right)^2$ have only one value $\displaystyle 2$.

However, $\displaystyle \sqrt{x^2}=2$ has two solutions.
Whereas, $\displaystyle \left(\sqrt{x}\right)^2=2$ has only one solution.
I would add that the former has only 2 REAL solutions and latter has only one REAL solution. If we're including imaginary solutions, it's a whole different ball game