Giải:
\(A=\sqrt{13+30\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
\(\Leftrightarrow A=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}\right)^2+4\sqrt{2}+1^2}}}\)
\(\Leftrightarrow A=\sqrt{13+30\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}\)
\(\Leftrightarrow A=\sqrt{13+30\sqrt{2+2\sqrt{2}+1^2}}\)
\(\Leftrightarrow A=\sqrt{13+30\sqrt{\left(\sqrt{2}\right)^2+2\sqrt{2}+1^2}}\)
\(\Leftrightarrow A=\sqrt{13+30\sqrt{\left(\sqrt{2}+1\right)^2}}\)
\(\Leftrightarrow A=\sqrt{13+30\left(\sqrt{2}+1\right)}\)
\(\Leftrightarrow A=\sqrt{5^2+2.5.3\sqrt{2}+\left(3\sqrt{2}\right)^2}\)
\(\Leftrightarrow A=\sqrt{\left(5+3\sqrt{2}\right)^2}\)
\(\Leftrightarrow A=5+3\sqrt{2}^2\)
Vậy ...
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