How would you do this (1 Viewer)

[Run hard@thehsc]

I used contradiction and got some sketchy proof which I am not sure is valid - how would you guys go about this?

 

[5uckerberg]

Let me give you a clue. Have you tried proving that is irrational through contradiction where n is a non-square number? Use that and then add some random rational number

 

[Drongoski]

Suppose to the contrary: rational number + irrational number = rational number . . . . (*)

i.e. R1 + IR = R2

i.e. m/n + IR = r/s where m,n,r,s are integers

.: IR = r/s - m/n = (nr - ms)/ns = integer/integer (a rational number)

.: an irrational number is a rational number

This is a contradiction

Therefore initial proposition (*) cannot be correct.