Question

prove the following as rational or irrational numbers.
1. (3+√2)^2
2. (4-√2)(4+√2)
3. (√11+√3)(√11-√3)
4. (2+√3)(3-√5)
5. 1/3+√2
6.22/7
7.π​

Answer 1

Answer:

Since both q and r are odd, we can write q=2m−1 and r=2n−1 for some m,n∈N. We note that the lefthand side of this equation is even, while the righthand side of this equation is odd, which is a contradiction. Therefore there exists no rational number r such that r2=3. Hence the root of 3 is an irrational number.