I already posted this on another thread and then found this one! How good!
Here's my problem...
Assume we know that √2 is irrational,
let x,y be any rational number such that y is not 0. Show that x + y√2 is irrational
Any help would be awesome!
I already posted this on another thread and then found this one! How good!
Here's my problem...
Assume we know that √2 is irrational,
let x,y be any rational number such that y is not 0. Show that x + y√2 is irrational
Any help would be awesome!
well, assume it is rational..
then for and integers, .. solving for we have .. since the set rational numbers is a field (i.e. closed under addition and multiplication, and defined for non-zero divisor) the right hand side of the equality is still a rational which is a contradiction to the assumption that is irrational.