Suppose that a and b are positive integers such that ${a}^{2}=3{b}^{2}$. Show that $0<b<a<2b$ and $(3b-a{)}^{2}=3(a-b{)}^{2}$

Use these and the Well-Ordering Principle to prove that no such a and b exist. From this it follows that $\sqrt{3}\notin \mathbb{Q}$.

Use these and the Well-Ordering Principle to prove that no such a and b exist. From this it follows that $\sqrt{3}\notin \mathbb{Q}$.