TITLE: how to simplify $ 2 \sqrt{2}\left(\sqrt{9-\sqrt{77}} \right) $
QUESTION [6 upvotes]: How to simplify
$$
2 \sqrt{2}\left(\sqrt{9-\sqrt{77}} \right)
$$
so that it has no nested radicals?
This question is same as that already posted but with a different point of view.

REPLY [4 votes]: $$2\sqrt{2}\sqrt{9-\sqrt{77}} = 2\sqrt{18-2\sqrt{7\cdot 11}} = 2\sqrt{(\sqrt{11}-\sqrt{7})^2} = 2\sqrt{11}-2\sqrt{7}.$$