Question

prove that root 2 is irrational ?

Answer 1

let root 2 be rational
root 2 = a/b                   (where a and b are co-primes)
squaring both sides 
2 = a^2/b^2
a^2 = 2b^2                 ............1)
let a = 2c
a^2 = 4c^2                 .............2)
now putting equation 2 in 1
2b^2 = 4c^2
b^2 = 2c^2                 ..............3)
from equation 1 and 2 we get that a and b have common factors .
so our contradiction is wrong 
therefore root 2 is irrational . 

Answer 2

assume that root 2 is a rational number
root 2 is a rational number an rational no. then it can be written in the form of p by q
_/2=p/q
squaring both sides we will get root 2 square is equal to p/Q square where p and q have no common factor
so p square will be equal to 2 q square mark this as equation 1
so we'll get that p square is an even number or P is an even number
Bangla for the value of p as 2K
So 2Q square is equal to 2 k ^2

2 q square is equal to 4 k square
Q square is equal to 2 k ^2

this implies that q is also an even number
so here's appears and contradiction that p and q are even numbers so they would have in common factor
so root 2 is an irrational number
I hope this might have you have attached a sheet and this might help you
which will in knowing more than your class notes might give you