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Math Help - Just a another one of those problems :)

  1. #1
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    Just a another one of those problems :)

    Hey guys im glad i found this site!


    With a and b as irrationals, is it possible for their sum or difference to be rational? Give a convincing argument for your response.


    Is it possible for a^b to be rational? Give a convincing argument.
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  2. #2
    Lord of certain Rings
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    Hey guys im glad i found this site!


    With a and b as irrationals, is it possible for their sum or difference to be rational? Give a convincing argument for your response.
    \color{red} \sqrt{2} + {(-\sqrt{2})} = 0 \in \mathbb{Q}
    \color{red}\sqrt{2} - {\sqrt{2}} = 0 \in \mathbb{Q}

    Is it possible for a^b to be rational? Give a convincing argument.

    \color{red}(2^{\sqrt{2}})^{\sqrt{2}} = 4 \in \mathbb{Q}
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  3. #3
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    Im not sure my teacher would let me right E Q in my anwser because i have no idea what that means
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  4. #4
    Flow Master
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    Quote Originally Posted by Bradley55 View Post
    Im not sure my teacher would let me right E Q in my anwser because i have no idea what that means
    Q is the symbol for rational numbers.
    E is the symbol for "is an element of".

    All Isomorphism is saying with this notation is that 0 and 4 are rational numbers ......

    Isomorphism has given you a couple of examples of values of a and b that clearly and convincingly show the answer to both questions is yes.

    (For the second part, "Is it possible for a^b to be rational", if your teacher wants you to prove that a = 2^{\sqrt{2}} is irrational, just smirk and refer him/her to the Gelfond-Schneider Theorem ......)
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