《中学生数学》04年3月(上)期P30刊登了3~(1/3)是无理数的证明”,读后颇受启发,但感到邓老师的证法有点繁,现首先给出如下简证: 证明假设3~(1/3)=q/p,P,q互质,平方整理得3p2=q2 若q=3n+1(n∈N),则q2=9n2+3n+1; “Middle school mathematics” published in March 2004 (the previous) period P30 published 3 ~ (1/3) is an irrational number of proof ", after reading very inspired, but feel that Deng’s proof is a bit complicated, is now given as follows Certificate: Prove that the hypothesis 3 ~ (1/3) = q / p, P, q coprime, squared to get 3p2 = q2 If q = 3n +1 (n ∈ N), then q2 = 9n2 + 3n +1;