InterviewSolution
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InterviewSolution
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Prove √2 is irrational |
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Answer» Yes Let us assume √2 is rational number.a rational number can be written into he form of p/q√2=p/qp=√2qSquaring on both sidesp²=2q²__________(1).·.2 divides p² then 2 also divides p.·.p is an even numberLet p=2a (definition of even number,\'a\' is positive integer)Put p=2a in eq (1)p²=2q²(2a)²=2q²4a²=2q²q²=2a².·.2 divides q² then 2 also divides qBoth p and q have 2 as common factor.But this contradicts the fact that p and q are co primes or integers.Our supposition is false.·.√2 is an irrational number. |
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