Firstly , let assume that root 2 is rational then,Root 2=p/q , now square both sideRoot 2square=p square/q square2=p square/q square =Q square =p square (This is first equation.)Now, p is divisible by (2)Let p =2k. (Here we use any word like i use k i also use x,y,z ). (This is second equation,).From (1 )&(2)Q square=(2k) square/2Q sq=4k square ( only this square is put on the k value )Q sq /2=k sqP/q is rational The common factor of p&q should be 1 Let we proved the common factor of p&q is( 2 ) this contradction occur due to our wrong assumption so,Root 2 is irrational , thanks for ask this question