Question:

Let $\sqrt{5} = p/q$ where $p, q$ are coprime integers ($q
eq 0$). Then $5q^2 = p^2 \Rightarrow p^2$ is divisible by $5 \Rightarrow p$ is divisible by $5$. Let $p = 5k$, then $25k^2 = 5q^2 \Rightarrow q^2 = 5k^2 \Rightarrow q$ is divisible by $5$. This contradicts coprimality. Hence $\sqrt{5}$ is irrational. [2.0 Marks]