Show with proof which of these two values is smaller: $7$, or $\sqrt 2+\sqrt 5 + \sqrt {11}$

Show with proof which of these two values is smaller:

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

I know this problem could be solved using numerous different methods but I am going to post my solution anyway, since I think and I believe I have done a great job in proving it using the most elementary method and the best of observation and thus it earned a place at this blog. :D