Prove that 1/2 is irrational

1.	Prove that 1/2 is irrational
Answer» Thanks 1/2 is not an irrational number To prove 1/√2 is irrationalLet us assume that\xa0√2 is irrational\xa01/√2 = p/q\xa0(where p and q are co prime)q/p =\xa0√2q =\xa0√2psquaring both sidesq² = 2p² .....................(1)By theorem\xa0q is divisible by 2∴ q = 2c ( where c is an integer)\xa0putting the value of q in equitation 12p² = q² = 2c² =4c²p² =4c² /2 = 2c²p²/2 = c²\xa0by theorem p is also divisible by 2But p and q are coprimeThis is a contradiction which has arisen due to our wrong assumption∴1/√2 is irrational

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