Another method to prove $7 ≥ \sqrt 2+\sqrt 5 + \sqrt {11}$

Show with proof which of these two values is smaller:

$7$, or $\sqrt 2+\sqrt 5 + \sqrt {11}$

In my (few) previous blog post (Which is greater), I mentioned of how I proved for $\sqrt 2+\sqrt 5 + \sqrt {11}$ is smaller than $7$.

But that doesn't mean that solution is the only way out to prove for that kind of problem.