问一个证明题，能用英文回答更好

1 Assume that the sum of√2 and√3 is a rational number.
假设√2+√3是一个有理数

2 So (√2+√3) could be express as p/q that both of p and q are integers, p/q is a fraction in lowest terms.
那么√2+√3可以被表示为一个最简分数p/q,p,q均为整数

3 Square both side.
So 2+3+2√6 = p^2/q^2
两边平方
则5+2√6=p^2/q^2

4 5+2√6 is a irrational number , so p^2/q^2 must be a irrational number.
因为5+2√6是一个无理数，那么 p^2/q^2 也是一个无理数

5 Because of both p and q are integers, so both p^2 and q^2 are integers and p/q is a fraction in lowest terms, so p^2/q^2 is also a fraction in lowest terms. But a irrational number can not be express as a fraction in lowest terms, it's contrary with 4.
由于p和q都是整数，所以p^2和q^2也都是整数, 且p/q是一个最简分数， 所以p^2/q^2是一个最简分数, 但是一个无理数不可能被表达为一个最简分数,这和结论(4)相矛盾

6 So √2+√3 is not a rational number.
It's a irrational number.

所以√2+√3不是一个有理数
是一个无理数

全部手写..英语可能有少量错误..
同学....这东西真的很费劲哎..- -|||
想必你也是某个出国班的