i need to find some proof that the SQRT of 2 is irational, where do i start and how is it irrational ?
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i need to find some proof that the SQRT of 2 is irational, where do i start and how is it irrational ?
You mean besides putting it in a calculator and getting an obviously irrational number?
lets see if i could come up with the proof:
let sqrt(2)=m/n, where m,n are positive integers and they are relative prime.
2=m^2/n^2
but as stated before m,n are relatively prime. so n^2=1, therefore m^2=2, which yields m=sqrt(2). that contradicts with m being an integers. therefore sqrt(2) cannot be represented by the quotient of two relatively prime integers. therefore sqrt(2) is irrational.