I got (i) simplified to 12 + sq.rt35 + sq.rt35
(ii) How would you know if it is irrational without a calculator?
$\displaystyle (\sqrt{7}+\sqrt{5})^2=7+5+2\sqrt{7}\cdot\sqrt{5}=1 2+2\sqrt{35}$.
Suppose that $\displaystyle 12+2\sqrt{35}\in\mathbf{Q}$.
Let $\displaystyle q\in\mathbf{Q}$ such as $\displaystyle 12+2\sqrt{35}=q\Rightarrow \sqrt{35}=\frac{q-12}{2}\in\mathbf{Q}\Rightarrow \sqrt{35}\in\mathbf{Q}$, false.
So $\displaystyle 12+2\sqrt{35}\not\in\mathbf{Q}$.