Lời giải:
1.
\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{(\sqrt{20}-\sqrt{9})^2}}}\)
\(=\sqrt{\sqrt{5}-\sqrt{3-(\sqrt{20}-\sqrt{9})}}=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)
\(=\sqrt{\sqrt{5}-\sqrt{(\sqrt{5}-1)^2}}=\sqrt{\sqrt{5}-(\sqrt{5}-1)}=\sqrt{1}=1\)
2.
\(A=\left[\frac{\sqrt{7}(\sqrt{2}-1)}{\sqrt{2}-1}-\frac{\sqrt{5}(\sqrt{3}-1)}{\sqrt{3}-1}\right].(\sqrt{7}+\sqrt{5})\)
\(=(\sqrt{7}-\sqrt{5})(\sqrt{7}+\sqrt{5})=7-5=2\)
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