Prove that √2 is irrational number?
The question you have asked is wrong it is not to prove 2 is irrational , it is to prove that root 2 is irrational
2 is not a irrational number
Dont ask silly questions ???????
I think its Root 2
Get it from rd sharma
Sorry, if you are not agree with me??
Here mathematical language is little bit tough to type
Yar you have to got it from rs aggarwal book.
Prove that 0 is a irrational
Let us assume √2 is rational number.a rational number can be written into he form of p/q√2=p/qp=√2qSquaring on both sidesp²=2q²__________(1).·.2 divides p² then 2 also divides p.·.p is an even numberLet p=2a (definition of even number,\’a\’ is positive integer)Put p=2a in eq (1)p²=2q²(2a)²=2q²4a²=2q²q²=2a².·.2 divides q² then 2 also divides qBoth p and q have 2 as common factor.But this contradicts the fact that p and q are co primes or integers.Our supposition is false.·.√2 is an irrational number.\xa0
Proof:let us assume √2 is an rational number.Therfore,√2=p/q where p and q are coprime and q is not equal to 0P= √2qSquaring on both sides,(P)square=(√2)squarePsquare=2squareTherefore,qsquare =psquare/2Psquare is divisible by 2P is also divisible by 2. {Equation 1}Let p=2k where k is some constant√2q=2kSquaring on both sides,√2qsquare=2ksquareKsquare=qsquare/2Therefore,qsquare is divisible by 2q is also divisible by 2. {Equation 2}From equation 1 and 2,P and q divides by 2 other than 1This is contradictory to our assumption that p and q are co primesTherefore, √2 is a irrational number
see R.S Aggrawal example