Prove that 1+1/√2 is irrational

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Solution

Let us assume 1+1/√2 is rational

So it can be expressed like 1+1/√2 = a/b
1-a/b = 1/√2
b-a/b = 1/√2
b/b-a = √2

Rational not = irrational

So our assumption is wrong 1+1/√2 is irrational

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