Question

$\sqrt{9 - 4 \sqrt{5 + \sqrt{14 - 6 \sqrt{5} } } }$

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Answer 1

$\sqrt{9-4\sqrt{5+\sqrt{14-6\sqrt{5}}}}=\sqrt{9-4\sqrt{5+\sqrt{(3-\sqrt{5})^2}}}=\sqrt{9-4\sqrt{5+3-\sqrt{5}}}\\ \\ =\sqrt{9-4\sqrt{8-\sqrt{5}}}.$