Elementary math proof

[lolo94]

Homework Statement

Proof 2/5*(2^0.5)-1/7 is irrational

Homework Equations

The Attempt at a Solution

I did this by splitting the expression and setting contradictions
2/5->rational
2^0.5->irrational

Proof first rational times irrational is irrational

Proof by contradiction

Assume the product is rational
let rational be x/y irrational s and the product u/t

rational*irrational=x/y*s=u/t
s=uy/tx

Contradiction s can't be rational

and then I do the same thing for irrational-rational

Is that the right approach?

 

[Ken G]

Sure-- a proof is a proof, and that would prove it. The question I have is if you are allowed to take as given that the square root of 2 is irrational, but if you are, proof by contradiction is certainly the way to go.