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Math Help - Even Func and Irrationality

  1. #1
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    Even Func and Irrationality

    Hello, I have questions regarding:

    a) Let k be any integer. Prove that if k^3 is even, then k is even.

    b) Prove that 3√2 is irrational. Hint: Mimic the proof that √2 is irrational and apply the result from part (a).

    c) Suppose two numbers a and b are irrational. Must the sum a + b be irrational? Justify your answer with an appropriate proof or counterexample


    Thanks for helping
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  2. #2
    Senior Member apcalculus's Avatar
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    Quote Originally Posted by mms6 View Post
    Hello, I have questions regarding:

    a) Let k be any integer. Prove that if k^3 is even, then k is even.

    b) Prove that 3√2 is irrational. Hint: Mimic the proof that √2 is irrational and apply the result from part (a).

    c) Suppose two numbers a and b are irrational. Must the sum a + b be irrational? Justify your answer with an appropriate proof or counterexample


    Thanks for helping
    a) Prove the contrapositive. Assuming k is odd, prove that k^3 is also odd.

    c) a = 1 - \sqrt{2} and   b = 1 + \sqrt{2}
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