Chapter 4.4, Problem 17E

(a)

To determine

To prove: That $\sqrt{2}$ is irrational using the result of Problem 23 that is, show that it is impossible to write $\sqrt{2}=\frac{a}{b}$ for integers $a,b.$

(b)

To determine

To prove: That $\sqrt{n}$ is irrationalusing the result of Problem 23 where $n$ is a natural numbersuch that $n\equiv 2(\mathrm{mod}3)$.