2 / root 3 = ( 2* root 3) / (root 3*root 3) , root 3*root 3 =3
= (2*root 3) / 3
= (2 / 3) * root 3 , 2/3 is a rational number ,root 3 is an irrational number
The product of a non-zero rational number and an irrational number is irrational.
2/root 3 is irrational