Question

show that root 3 is irrational

Answer 1

let us assume that √3 is rational
√3 = a/b where a and b are co prime
√3 b = a
sq. both the sides 
3 = a²/b²
3 b² = a² 
so 3 factor a²
     3 divide a²
     3 divide a also
now
a = 3 c for c = integer
sq. both side 
a² = 3 c²

from 1
3 b² = 9 c²
b² = 3 c²
now b also factor of 3 
but we assumed that a and b are co prime this is because of our wrong initial assumption that √3 is rational


H.P