# Thread: Irrational Numbers q+a

1. ## Irrational Numbers q+a

Let q belong to Q, and a belong to R\Q. Prove

q+a is irrational

so you let q = m/n

Not sure how to go about solving this, thanks

2. Originally Posted by glover_m
Let q belong to Q, and a belong to R\Q. Prove

q+a is irrational

so you let q = m/n

Not sure how to go about solving this, thanks
You can use contradiction :

suppose q +a is rational ====> q+a=x/y where x,y are integers ,but also q is rational so q=z/w ,where again z,w are integers ,hence:

..............a= x/y -z/w a rational ,thus contradiction