Prove that 2+√3 is irrational
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therefore 2+√3 is irrational
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Let us assume to the contrary, that 2+√3 is rational
where a and b are integers where b is not equal to zero. Such that 2+√3=a/b
where a and b are co-prime
Now,
2+√3=a/b
√3=a/2b
Since, 2, a and b are integers, a/2b is rational, and so √3 is rational. But this contradicts the fact that
√3 is irrational. This contradiction has arisen due to our wrong assumption that 2+√3 is rational.
Therefore we can conclude that 2+√3 is irrational.
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