Solution:

Let’s say that $p$ is false, as sum of an irrational no. and a rational no. is irrational.

Let $\sqrt{\lambda }$ is irrational and $n$ is rational no.

$\sqrt{\lambda } + n = r$

$\sqrt{\lambda } = r – n$

But, it is known that $\sqrt{\lambda }$ is irrational whereas $(r-n)$ is rational which is a contradiction.

So here, our assumption is False.

As a result, $P$ is true.