Question

Prove that route3 is a irrational no.

Answer 1

let root 3 be a raional number(hello can i represent root 3 by _3)
_3=p/q where p and q are are integers, q is not equal to zero and they are co prime
3=p^2/q^2
3q^2=p^2
hence p is multiple of 3
p=3k where k is an integer
p^2=9k^2
hence we find that
q^2=3k^2
q is a multiple of 3
now if both p and q are multiple of three, then they are not in perfect fraction or co prime mode, hence our assumption was wrong