Check for reflexivity:

As $3(a-a)+\sqrt{7}=\sqrt{7}$ which belongs to relation so relation is reflexive

Check for symmetric:

Take $a=\frac{\sqrt{7}}{3}, b=0$

Now $(a, b) \in R$ but $(b, a) \notin R$

As $3(b-a)+\sqrt{7}=0$ which is rational so relation is not symmetric.

Check for Transitivity:

Take $(a, b)$ as $\left(\frac{\sqrt{7}}{3}, 1\right)$

$\&(b, c)$ as $\left(1, \frac{2 \sqrt{7}}{3}\right)$

So now $( a , b ) \in R \&( b , c ) \in R$ but $( a , c ) \notin R$ which means relation is not transitive