Use the Well-ordering Principle to Prove √3 Is Irrational

Use the Well-ordering Principle to Prove √3 Is Irrational.

[andreben]

This is the most elementary yet the most surprising proof I know of the irrationality of square roots of non-perfect square numbers.

[mosaadalabdullatif]

p and q could be both positive or both negative, so we may assume WLOG they are both positive.

[Alex-xumo]

as i understand it only works for sqrt2 or sqrt3 as if we have higher square roots (sqrta-1)>1 and so (sqrta-1)m>m so there should be different methods for proving that other sqrt are not rational?

[ddsharma]

This is standard 6 maths question in india