prove that 7+√2 is irrational
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10
Answer:
let us assume on the contrary that 7+√2 is rational
that is, we can find co-prime a and b (#0) such that 7+√2=a/b
therefore,
7-a/b = √2
since a&b are integers so 7- a/b is a rational number so, √2 is rational
But this contradicts the fact that √2 is irrational
The contradiction has arisen due to our incorrect assumptions that 7+√2 is irrational
so,
we conclude that 7+√2 is irrational
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