let us assume root p is a rational number then
root p =a/b
squaring on both the sides
p=A square/B square
B square=A square/p
since A square is divisible by p , A is also divisible by p
let us take A=pm then
B square=p2m2/p NOTE; (2 is nothing but square)
B2=pm2
M2=B2/p
since B2 is divisible by p ,B is also divisible by p
since both A and B have common factor as p
my assumsion is wrong
therefore root p is an irrational number
Written on Jan. 27, 2018, 12:30 p.m.