Prove √2 is irrational

  • Thread starter Jamin2112
  • Start date
  • #1
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Homework Statement



As the title says.

Homework 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

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.
 

Answers and Replies

  • #2
Petek
Gold Member
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Your proof is correct!
 

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