Đáp án+Giải thích các bước giải:
\(a.\\\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\\= \sqrt{\sqrt{5}-\sqrt{3-\sqrt{(3-2\sqrt{5})^2}}}\\=\sqrt{\sqrt{5}-\sqrt{3-(2\sqrt{5}-3)}}\\=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\\=\sqrt{\sqrt{5}-\sqrt{(1-\sqrt{5})^2}}\\= \sqrt{\sqrt{5}-(\sqrt{5}-1)}\\=\sqrt{1}=1\\b.\\\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\\=\sqrt{13+30\sqrt{2+\sqrt{(1+2\sqrt{2})^2}}}\\=\sqrt{13+30\sqrt{2+1+2\sqrt{2}}}\\=\sqrt{13+30\sqrt{(\sqrt{2}+1)^2}}\\= \sqrt{13+30(\sqrt{2}+1)}\\=\sqrt{13+30\sqrt{2}+30}\\=\sqrt{43+30\sqrt{2}}\\=\sqrt{25+30\sqrt{2}+18}\\=\sqrt{(5+3\sqrt{2})^2}=5+3\sqrt{2}\\c.\\(\sqrt{3}-\sqrt{2})\sqrt{5+2\sqrt{6}}\\=(\sqrt{3}-\sqrt{2})\sqrt{(\sqrt{2}+\sqrt{3})^2}\\=(\sqrt{3}-\sqrt{2})(\sqrt{2}+\sqrt{3})\\=3-2\\=1\)