\(\sqrt{12-2\sqrt{14+2\sqrt{13}}}\)
\(=\sqrt{12-2\sqrt{\left(\sqrt{13}\right)^2+2\sqrt{13}+1}}\)
\(=\sqrt{12-2\sqrt{\left(\sqrt{13}+1\right)^2}}\)
\(=\sqrt{12-2.\left|\sqrt{13}+1\right|}\)
\(=\sqrt{12-2\left(\sqrt{13}+1\right)}\)
\(=\sqrt{12-2\sqrt{13}+2}\)
\(=\sqrt{14+2\sqrt{13}}\)
\(=\sqrt{\left(\sqrt{13}\right)^2+2\sqrt{13}+1}\)
\(=\sqrt{\left(\sqrt{13}+1\right)^2}\)
\(=\left|\sqrt{13}+1\right|\)
\(=\sqrt{13}+1\) ( vi \(\sqrt{13}+1>0\))
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