Question

proof sqrt 2 is irrational no.

Answer 1

google it and find one you like and understand. there are very very many

Answer 2

try finding a and b such that a/b = \sqrt{2}

Answer 3

i want a formal proof

Answer 4

my favorite uses the method of infinite descent, and in fact all of them use that. each one starts by "suppose it is rational" so
\[\sqrt{2}=\frac{a}{b}\iff 2=\frac{a^2}{b^2}\iff 2b^2=a^2\] and then you can find many reasons why this cannot be true for whole numbers a and b

Answer 5

really google is your best friend on this one. you will find many reasons that one integer squared cannot be twice another integer squared

Answer 6

ya its true but how it concludes to being irrational.?

Answer 7

2b^2 = a^2 means that 2 is a factor of a^2, and subsequently a factor of a

Answer 8

so

Answer 9

so that means a/b has a factor of 2

Answer 10

this ultimately contradicts the assumption that a/b = \sqrt{2}