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Answer 1

$1)\sqrt{6-2\sqrt{5}}-\sqrt{9+4\sqrt{5}}=\sqrt{5-2\sqrt{5}+1 } -\sqrt{5+4\sqrt{5}+4}=\sqrt{(\sqrt{5})^{2}-2\sqrt{5}+1^{2}} -\sqrt{(\sqrt{5})^{2}+4\sqrt{5} +2^{2}}=\sqrt{(\sqrt{5}-1)^{2}}-\sqrt{(\sqrt{5}+2)^{2}}=|\sqrt{5}-1|-|\sqrt{5}+2)=(\sqrt{5}-1)-(\sqrt{5}+2)=\sqrt{5}-1-\sqrt{5}-2=-3\\\\Otvet:\boxed{-3}$

$2)\sqrt{29-4\sqrt{7}}-2\sqrt{11-4\sqrt{7}}= \sqrt{1-4\sqrt{7} +28}-2\sqrt{4-4\sqrt{7}+7}=\sqrt{1^{2}-4\sqrt{7}+(2\sqrt{7})^{2}}-2\sqrt{2^{2}-4\sqrt{7}+(\sqrt{7})^{2}}=\sqrt{(1-2\sqrt{7})^{2}}-2\sqrt{(2-\sqrt{7})^{2}}=|1-2\sqrt{7}|-2|2-\sqrt{7} |=(2\sqrt{7}-1)-2(\sqrt{7}-2)=2\sqrt{7} -1-2\sqrt{7}+4=3\\\\Otvet:\boxed{3}$