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Prove that 5/3√2 is an irrational number? |
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Answer» It is irrationalStep-by-step EXPLANATION:Let us assume the contrary.i.e; 5 + 3√2 is rational∴ 5 + 3√2 = ab, where ‘a’ and ‘B’ are COPRIME integers and b ≠ 03√2 = ab – 53√2 = a−5bbOr √2 = a−5b3bBecause ‘a’ and ‘b’ are integers a−5b3b is rationalThat contradicts the fact that √2 is irrational.The CONTRADICTION is because of the INCORRECT assumption that (5 + 3√2) is rational.So, 5 + 3√2 is irrational. |
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