Question

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Answer 1

$( \sqrt{2} -1) \sqrt{4+ \sqrt{9-4\sqrt{2}} } =(\sqrt{2}-1) \sqrt{4+ \sqrt{(2\sqrt{2}-1)^2} } = \\ =(\sqrt{2}-1) \sqrt{3+2\sqrt{2}} =(\sqrt{2}-1) \sqrt{(\sqrt{2}+1)^2} =(\sqrt{2}-1)(\sqrt{2}+1)=2-1=1$