Question

Prove √2 is not a rational number
please give detailed Explanation​

Answer 1

Answer:

let us assume ,

√2 is rational .

we can find integer p and ( q ≠ 0 )

= √2 = p/q

suppose p and q have common factor other than 1 . then we divided by the common factor to get √2= a/b where a and b are coprime .

So ,

=b√2=a

squaring on both side and rearranging .

we get ,

= 2b²=a²

we can write

a=2c

substituting for a ,

2b²=4c²

b²=2c²

this means that 2 divides b²

Therefore , a and b have at least 2 as a common factor .

√2 is irrational number .