Prove that 1upon root 2 is irrational

1.	Prove that 1upon root 2 is irrational
Answer» We assume that 1/{tex}\\sqrt2{/tex} is a rational noSo\xa0{tex}\\frac ab=\\frac{1}{\\sqrt2}{/tex}( Where and\xa0b are co-primes)b=a{tex}\\sqrt 2{/tex}b2=2a2--------(1)b2 is divisible by 2 ,so b is divisible by 2-----(2)Let b=2c( c is any integer)b2=4c22a2=4c2a2=2c2So a2 is divisible by 2,So a is divisible by 2-----(3)From (2) and (3)\xa0a and b are divisible by 2But this contradict the assumption\xa0that a and b are co-prime ,So no common factor in and b except 1Hence our assumption that 1/\xa0{tex}\\sqrt2{/tex}\xa0is wrong ,Hence 1/{tex}\\sqrt2{/tex} is a non prime number-

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