Proofs of Irrationality
A short proof of the irrationality of can be obtained from the rational root theorem, that is, if is a monic polynomial with integer coefficients, then any rational root of is necessarily an integer. Applying this to the polynomial, it follows that is either an integer or irrational. Because is not an integer (2 is not a perfect square), must therefore be irrational.
See quadratic irrational or infinite descent#Irrationality of √k if it is not an integer for a proof that the square root of any non-square natural number is irrational.
Read more about this topic: Square Root Of 2
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