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## 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?