Question 1130147: Using proof by contradiction, show that (3+√2)/3 is irrational.
Answer by math_helper(2461)   (Show Source):
You can put this solution on YOUR website! I will assume that we accept  as irrational (proof provided at the end, for completeness):
Assume  where p,q are relatively prime integers, both greater than zero
Write 3p as P, where P is obviously also an integer:
Re-arrange:
The RHS is integer minus integer, which must produce another integer (integers are closed under subtraction). Call it R:
 where R and q are integers, a contradiction.
Therefore,  is irrational.
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Proof that is irrational:
 p,q relatively prime integers
LHS is even —> RHS must also be even, but this contradicts p,q being relatively prime. Thus  is irrational.
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