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Math Help - absolute value

  1. #1
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    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
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  2. #2
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    Quote Originally Posted by billq View Post
    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 \sqrt{2^2}~\&~\left(\sqrt2\right)^2 have only one value 2.

    However, \sqrt{x^2}=2 has two solutions.
    Whereas, \left(\sqrt{x}\right)^2=2 has only one solution.
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  3. #3
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    Quote Originally Posted by Plato View Post
    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 \sqrt{2^2}~\&~\left(\sqrt2\right)^2 have only one value 2.

    However, \sqrt{x^2}=2 has two solutions.
    Whereas, \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
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