Chapter 8.4, Problem 25E

(a)

To determine

To prove: $\sqrt{p}$ is irrational by examining $f\left(x\right)=x^2-p\in \mathbb{Q}\left[x\right]$ where $p$ be a prime.

(b)

To determine

To prove: There exist irreducible polynomials of every positive degree in $\mathbb{Q}\left[x\right]$.