Proof that the square root of 2 is irrational

Pythagoras and his followers hated the idea that the square root of 2 is irrational but it’s an easy enough fact to prove.

[asbarker]

I really enjoyed this version of the proof. I've never seen it done by using the Fundamental Theorem of Arithmetic, but this approach works really well - and is rigorous.

[gedlangosz]

Great video! I had only seen this proved before by showing that both a&b must be even, and hence a contradiction. I like thus version - thank you.

[hamzahamxa]

Thank you
are you discovered this proof ?

[brettcraigsly]

A little off subject... but, If you use the Pythagorean theorem with sides a and be equaling 1, so hypotenuse is root 2, and you perfectly drew this right triangle on paper... the hypotenuse mathematically is an irrational number, meaning infinite decimal places, right? So how could a physically drawn or constructed triangle have a side whose measurement has infinite decimal places in its measurement? If you began trying to physically measure the root 2 side with a ruler with Planck length marks, would it have a limited length of Planck length units? And you could no longer subdivide those, so if the decimal places go on forever mathematically, but a true physical measurement would be finite. ... I am not a physicist or mathematician. So I may not being picturing it correctly. But it would seem like you have a mathematical principle that is not physically reproducible in the physical world. Is that right? Asking for a friend.