a) \(\left(\sqrt{3}-1\right).\sqrt{2.\sqrt{19+8\sqrt{3}}-4}\)
b) \(\sqrt{5+2\sqrt{6}}+\sqrt{14-4\sqrt{6}}\)
c)\(\sqrt{5-2\sqrt{6}}+\sqrt{11-4\sqrt{6}}\)
d) \(\sqrt{23+6\sqrt{10}}+\sqrt{47+6\sqrt{10}}\)
e) \(\sqrt{21-6\sqrt{10}}+\sqrt{21+6\sqrt{10}}\)
a, \(\left(\sqrt{3}-1\right).\sqrt{2\sqrt{19+8\sqrt{3}-4}}\)
\(=\left(\sqrt{3}-1\right)\sqrt{2.\left|4+\sqrt{3}\right|-4}=\left(\sqrt{3}-1\right)\sqrt{4+2\sqrt{3}}\)
\(=\left(\sqrt{3}-1\right).\left(\sqrt{3}+1\right)=3-1=2\)
b, \(\sqrt{5+2\sqrt{6}}+\sqrt{14-4\sqrt{6}}\)
\(=\sqrt{5}+1+\sqrt{2\left(7-2\sqrt{6}\right)}\)
\(=\sqrt{5}+1+\sqrt{2\left(\sqrt{6}-1\right)^2}=\sqrt{5}+1+\sqrt{2}\left(\sqrt{6}-1\right)\)
\(=\sqrt{5}+1+\sqrt{12}-\sqrt{2}\)
c, \(\sqrt{5-2\sqrt{6}}+\sqrt{11-4\sqrt{6}}\)
ps : \(\sqrt{11-4\sqrt{6}}=\sqrt{11-2.2.\sqrt{2}\sqrt{3}}\)
\(=\sqrt{\left(2\sqrt{2}\right)^2-2.2\sqrt{2}\sqrt{3}+3}=\sqrt{\left(2\sqrt{2}-\sqrt{3}\right)^2}\)( viết hẳn ra sợ bạn thắc mắc >< )
\(=\sqrt{5}-1+2\sqrt{2}-\sqrt{3}\)