\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
\(=\sqrt{6+2\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}}\)
\(=\sqrt{6+2\sqrt{4-2\sqrt{3}}}\)
\(=\sqrt{6+2\sqrt{\left(\sqrt{3}-1\right)^2}}\)
\(=\sqrt{4+2\sqrt{3}}\)
\(=\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=\sqrt{3}+1\)
mik sẽ làm chi tiết, không hiểu thì mình thua.
\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
\(=\sqrt{6+2\sqrt{5-\sqrt{13+4\sqrt{3}}}}\)
\(=\sqrt{6+2\sqrt{5-\sqrt{\left(1+2\sqrt{3}\right)^2}}}\)
\(=\sqrt{6+2\sqrt{5-\left(1-2\sqrt{3}\right)}}\)
\(=\sqrt{6+2\sqrt{5-1-2\sqrt{3}}}\)
\(=\sqrt{6+2\sqrt{4-2\sqrt{3}}}\)
\(=\sqrt{6+2\sqrt{\left(1-\sqrt{3}\right)^2}}\)
\(=\sqrt{6+2\left(\sqrt{3}-1\right)}\)
\(=\sqrt{6+2\sqrt{3}-2}\)
\(=\sqrt{4+2\sqrt{3}}\)
\(=\sqrt{\left(1+\sqrt{3}\right)^2}\)
\(=1+\sqrt{3}\)
