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Prove √2 is irrational

  1. Oct 8, 2010 #1
    1. The problem statement, all variables and given/known data

    As the title says.

    2. Relevant equations

    Rational number: a/b for some integers a, b
    Even number: 2k for some integer k
    Odd number: 2j+1 for some integer j

    3. The attempt at a solution

    Assume √2 is a rational number. Then it can be expressed a/b for some integers a and b. Reduced to it’s lowest form, a and b cannot both be even numbers.

    √2 = a/b ----> √2b=a ----> 2b2=a2 ---->a2 is even ----> a is even ----> a=2k for some integer k ----> 2b2=(2k)2 ----> b2=2k2 ----> b is even: a contradiction because both a and b cannot be even.

    Hence √2 is not a rational number.
  2. jcsd
  3. Oct 8, 2010 #2
    Your proof is correct!
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