Proof:-let √3 is a rational number
Then √3=p/q
(where p and q have not a common factor and q is not equal to zero)
Squaring both side LHS and RHS
(√3)^2=(p/q)^2
3=p^2/q^2
3q^2=p^2
p^2=3q^2
3 divide p^2
then 3 divide p
Now again let p=3k
Square each side LHS and RHS
p^2=9k^2 ....... 2
From 1 and 2
3q^2=9k^2
q^2=3k^2
3 divide q^2
Then 3 divide q
Since 3 divide both p and q means p and q have a common factor but we believe that p and q have not common factor so our recognition is failed.
Hense √3 is not an rational number so √3 is an irrational number.
