Prove that 1\\√2is irrational

1.	Prove that 1\\√2is irrational
Answer» To prove 1/√2 is irrational.............Let us assume that\xa0√2 is irrational\xa0..........1/√2 = p/q\xa0(where p and q are co prime)........q/p =\xa0√2.........q =\xa0√2p.......squaring both sides.........q² = 2p² .....................(1)By theorem\xa0......q is divisible by 2.......∴ q = 2c ( where c is an integer).......\xa0putting the value of q in equitation 1.......2p² = q² = 2c² =4c² ......p² =4c² /2 = 2c².....p²/2 = c²\xa0.....by theorem p is also divisible by 2.....But p and q are coprime........This is a contradiction which has arisen due to our wrong assumption....∴1/√2 is irrational

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