$(\sqrt{3}+\sqrt{5})$
Let us assume that $(\sqrt{3}+\sqrt{5})$ is rational
On squaring , we get
$(\sqrt{3}+\sqrt{5})$ is rational
$\Rightarrow 3+2\sqrt{3}\times \sqrt{5}+5$ is rational
$\Rightarrow 8+2\sqrt{15}$ is rational
Subtract 8 from above result , considering 8 is a rational number.
as we know , difference of two national numbers is a rational.
$\Rightarrow 8+2\sqrt{15}-8$ is rational
$\Rightarrow 2\sqrt{15}$is rational
Which is only possible if 2 is rational and $\sqrt{15}$ is rational.
The fact is $\sqrt{15}$ is not a rational number.
Our assumption is wrong, and
$(\sqrt{3}+\sqrt{5})$ is irrational