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Prove that 1\\√2 is irrational |
| Answer» Let us assume, to the contrary, that is{tex}\\frac { 1 } { \\sqrt { 2 } }{/tex} rational.So, we can find coprime integers a and b\xa0{tex}( \\neq 0 ){/tex}\xa0such that{tex}\\frac { 1 } { \\sqrt { 2 } } = \\frac { a } { b } \\Rightarrow \\sqrt { 2 } = \\frac { b } { a }{/tex}Since, a and b are integers,\xa0{tex}\\frac { b } { a }{/tex}\xa0is rational, and so is{tex}\\sqrt { 2 }{/tex} rational.But this contradicts the fact that is{tex}\\sqrt { 2 }{/tex} irrational.So, we conclude that is{tex}\\frac { 1 } { \\sqrt { 2 } }{/tex} irrational. | |