证明：根号3 为无理数。

We assume that sqrt(3) is a rational number

==> since sqrt(3) is a rational number
we can find a smallest integer k such that k*sqrt(3) is also a integer.

now take m = k*sqrt(3)-k which is also a integer.

And m*sqrt(3) = (k*sqrt(3)-k) * sqrt(3) = 3k-sqrt(3)k is also an integer.

However, m = k*sqrt(3) -k is smaller than k.
And we claimed that k is the smallest integer that will make k*sqrt(3) an integer.
This is the contradiction.

We conclude that our assumption is false and sqrt(3) is irrational.

所谓无理数是指无限不循环小数
由于根号3是无限不循环小数 所以可以逆推出它是无理数

自己都觉得这样说不过去啦 呵呵 不好意思啊

反证法！

假设根号3是有理数，那么一定是有限小数或者是无限循环小数。

仅提供思路，希望对你有帮助^_^

所谓无理数是指无限不循环小数

把根号3开出来，是个无限不循环小数，那就是无理数撒

根号3我不会我见过根号2的好象用图象法能证出来啊！