show that 2+√2 is an irrational no.
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Step-by-step explanation:
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Step-by-step explanation:
By the method of contradiction, let 2+√2 be rational
therefore, 2+√2=a/b
√2=a/b-2
√2=a-2b (whole upon) b
Since, a,2 and b are integers,
therefore,a-2b (whole upon) b is rational and so √2 is rational
but this contradicts the fact that √2 is irrational.
this contradiction has arisen due to our incorrect assumption that 2+√2 is rational
therefore, 2+√2 is irrational
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