B= \(\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\sqrt{2}\)
C= \(\sqrt{4-\sqrt{7}}-\sqrt{4}+\sqrt{7}\)
D= \(\sqrt{3}-\sqrt{2}-\sqrt{\sqrt{3}+\sqrt{2}}\)
E= \(\sqrt{4+2\sqrt{2}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
F= \(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right)\sqrt{2}+2\sqrt{5}\)
G= \(\left(\sqrt{14}-\sqrt{10}\right).\left(\sqrt{6+\sqrt{35}}\right)\)
H= \(\sqrt{11-4\sqrt{7}}-\sqrt{2}.\sqrt{8+3\sqrt{7}}\)
Lời giải:
\(B=(\sqrt{2}-\sqrt{3-\sqrt{5}})\sqrt{2}=2-\sqrt{6-2\sqrt{5}}\)
\(=2-\sqrt{5+1-2\sqrt{5}}=2-\sqrt{(\sqrt{5}-1)^2}=2-(\sqrt{5}-1)=3-\sqrt{5}\)
\(C=\sqrt{4-\sqrt{7}}-\sqrt{4}+\sqrt{7}=\sqrt{\frac{8-2\sqrt{7}}{2}}-2+\sqrt{7}\)
\(=\sqrt{\frac{7+1-2\sqrt{7}}{2}}-2+\sqrt{7}\)
\(=\sqrt{\frac{(\sqrt{7}-1)^2}{2}}-2+\sqrt{7}\)
\(=\frac{|\sqrt{7}-1|}{\sqrt{2}}-2+\sqrt{7}=\frac{\sqrt{7}-1}{\sqrt{2}}-2+\sqrt{7}\)
$D$: bạn xem lại đề, mình thấy biểu thức không rút gọn được nữa.
\(E=\sqrt{4+2\sqrt{2}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)
\(=\sqrt{4+2\sqrt{2}}.\sqrt{2^2-(2+\sqrt{2})}\)
\(=\sqrt{4+2\sqrt{2}}.\sqrt{2-\sqrt{2}}=\sqrt{2}.\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2}}\)
\(=\sqrt{2}.\sqrt{2^2-(\sqrt{2})^2}=\sqrt{2}.\sqrt{2}=2\)
\(F=(\sqrt{2}-\sqrt{3+\sqrt{5}})\sqrt{2}+2\sqrt{5}\)
\(=2-\sqrt{6+2\sqrt{5}}+2\sqrt{5}\)
\(=2-\sqrt{5+1-2\sqrt{5}}+2\sqrt{5}\)
\(=2-\sqrt{(\sqrt{5}-1)^2}+2\sqrt{5}\)
\(=2-(\sqrt{5}-1)+2\sqrt{5}=3+\sqrt{5}\)
\(G=(\sqrt{14}-\sqrt{10}).\sqrt{6+\sqrt{35}}=\sqrt{2}(\sqrt{7}-\sqrt{5})\sqrt{6+\sqrt{35}}\)
\(=(\sqrt{7}-\sqrt{5})\sqrt{12+2\sqrt{35}}=(\sqrt{7}-\sqrt{5}).\sqrt{7+5+2\sqrt{7.5}}\)
\(=(\sqrt{7}-\sqrt{5}).\sqrt{(\sqrt{7}+\sqrt{5})^2}=(\sqrt{7}-\sqrt{5})(\sqrt{7}+\sqrt{5})=7-5=2\)
\(H=\sqrt{11-4\sqrt{7}}-\sqrt{2}.\sqrt{8+3\sqrt{7}}\)
\(=\sqrt{2^2+7-2.2.\sqrt{7}}-\sqrt{16+6\sqrt{7}}\)
\(=\sqrt{(2-\sqrt{7})^2}-\sqrt{3^2+7+2.3\sqrt{7}}=\sqrt{(2-\sqrt{7})^2}-\sqrt{(3+\sqrt{7})^2}\)
\(=|2-\sqrt{7}|-|3+\sqrt{7}|=\sqrt{7}-2-(3+\sqrt{7})=-5\)
