Question

prove that √2 is irrational by suitable method.

Answer 1

Let's suppose √2 is a rational number.

Then we can write it √2  = p/qwhere p,q are whole numbers, q not zero.

√√2=p/q

p=√2q

Squaring on both sides 

p²=2q²__________(1)

.·.2 divides p² then 2 also divides p

.·.p is an even number

Let p=2a (definition of even number,'a' is positive integer)

Put p=2a in eq (1)

p²=2q²

(2a)²=2q²

4a²=2q²

q²=2a²

.·.2 divides q² then 2 also divides q

Both 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.

hope it help 

Answer 2

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