Question

prove that root 2 is an irrational number using division long method

Answer 1

Let√2 be a rational no.
√2=p/q
squaring on both sides
2=p^2/q^2
p^2=2q^2
p^2 is divisible by 2
p is divisible by 2. ....(i)
.:Let p=2r for some positive integer r
=>p^2=4r^2
q^2=2r^2
q^2 is divisible by 2
q is divisible by 2. ....(ii)
From (i) and(ii) ,p and q are divisible by 2 which contradicts the fact that p and q are co-primes
Hence,our assumption is false
√2 is irrational