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Math Help - prove sqrt(3) + sqrt (5) is an irrational number

  1. #1
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    prove sqrt(3) + sqrt (5) is an irrational number

    Given that sqrt(15) is an irrational number, prove that sqrt(3) + sqrt (5) is an irrational number.

    Please teach me how to solve this question. Thank you very much.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by beta12 View Post
    Given that sqrt(15) is an irrational number, prove that sqrt(3) + sqrt (5) is an irrational number.

    Please teach me how to solve this question. Thank you very much.
    Suppose sqrt(3)+sqrt(5) is rational, then:

    (sqrt(3)+sqrt(5))^2=3+2sqrt(15)+5=8+2sqrt(15)

    is rational, which implies that sqrt(15) is rational - a contradiction.

    Hence sqrt(3)+sqrt)5) is irrational.

    RonL
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  3. #3
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    Hi Captainblack,

    Thank you very much.
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