Question

prove that following are irrational. 1/root2​

Answer 1

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Answer 2

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$we \:have \: to \: prove \: 1 \div \sqrt{2} \: is \: irrational \\ let \: us \: assume \: that \: 1 \div \sqrt{2} \: is \: rational \\ hence.1 \div \sqrt{2} \: cannot \: be \: written \: in \: the \: form \: a \div b \\ where \: a \: and \: b \: (b \: not = 0) \: are \: co-prime \\ (no \: common \: factor \: other \: than \: 1) \\ hence.1 \div \sqrt{2} = a\div \: b$

$b \div a = \sqrt{2} \\ here \: b \div a \: is \: rational \\ \sqrt{2} \: is \: irrational \\ since \: rational \: not \: equal \: to \:irrational \\ therefore \: our \: assumption \: is \: incorrect \\ hence \: 1 \div \sqrt{2} \: is \: irrational \\ hence \: proved$