Bài 1: Tính
1, \(A=\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right).\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
2, \(B=\left(\frac{3\sqrt{125}}{15}-\frac{10-4\sqrt{6}}{\sqrt{5}-2}\right).\frac{1}{\sqrt{5}}\)
3, \(C=\left(\frac{\sqrt{1000}}{100}-\frac{5\sqrt{2}-2\sqrt{5}}{2\sqrt{5}-8}\right).\frac{\sqrt{10}}{10}\)
4, \(D=\frac{1}{\sqrt{49+20\sqrt{6}}}-\frac{1}{\sqrt{49-20\sqrt{6}}}+\frac{1}{\sqrt{7-4\sqrt{3}}}\)
5, \(E=\frac{1}{\sqrt{4-2\sqrt{3}}}-\frac{1}{\sqrt{7-\sqrt{48}}}+\frac{3}{\sqrt{14-6\sqrt{5}}}\)
6, \(F=\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
7, \(G=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}-\sqrt{11-2\sqrt{10}}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}+\sqrt{12+8\sqrt{2}}}}\)
\(C=\dfrac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}}-\sqrt{11+2\sqrt{10}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}}+\sqrt{12+8\sqrt{2}}}\)
\(B=\dfrac{20}{3+\sqrt{5}+\sqrt{2+2\sqrt{5}}}\)
Tính B = \(\frac{1+xy}{x+y}-\frac{1-xy}{x-y}vớix=\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2+\sqrt{2}}}}y=\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
c) \(\left(\sqrt{10}+\sqrt{2}\right)\left(\sqrt{3+\sqrt{5}}\right)\left(6-2\sqrt{5}\right)\)
d) \(\sqrt{8+\sqrt{8}+\sqrt{20}+\sqrt{40}}-\sqrt{2}-\sqrt{5}\)
Bài 1:Thực hiện phép tính
1. \(\sqrt{27}-3\sqrt{48}-2\sqrt{75}-\sqrt{\left(2-\sqrt{3}\right)^2}\)
2.\(\left(\sqrt{8}-5\sqrt{2}+\sqrt{20}\right).\sqrt{5}+\left(40\sqrt{\frac{1}{10}}-10\right)\)
3.\(\left(\sqrt{24}-\sqrt{\frac{2}{3}}-\sqrt{\frac{1}{6}}+\sqrt{\frac{3}{2}}\right).\sqrt{6}\)
Tính:
\(A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}\)
\(B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}\)
\(C=10\sqrt{\dfrac{1}{5}}+\dfrac{1}{5}\sqrt{125}-2\sqrt{20}\)
\(E=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\)
\(F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
Tính:
\(A=3\sqrt{20}-\sqrt{45}+2\sqrt{18}+\sqrt{72}\)
\(B=\dfrac{12}{3-\sqrt{5}}-\dfrac{16}{\sqrt{5}+1}\)
\(C=10\sqrt{\dfrac{1}{5}}+\dfrac{1}{5}\sqrt{125}-2\sqrt{20}\)
\(E=\sqrt{\left(\sqrt{3}+1\right)^2}-\sqrt{\left(\sqrt{3}-2\right)^2}\)
\(F=\sqrt{6+2\sqrt{5}}-\sqrt{9-4\sqrt{5}}\)
Bài 1:Thực hiện phép tính
1.(\(\sqrt{28}_{ }-\sqrt{12}-\sqrt{7}\))\(\sqrt{7}\)+2\(\sqrt{21}\)
2. 2\(\sqrt{3}\) +\(\sqrt{27}\)-3\(\sqrt{45}\) +\(\sqrt{5}\)
3.(2\(\sqrt{2}\) -\(\sqrt{5}\)+\(\sqrt{18}\)).\(\sqrt{5}+20\sqrt{\frac{1}{10}}\)
4.\(\sqrt{27}-3\sqrt{48}+2\sqrt{75}-\sqrt{\left(2-\sqrt{3}\right)^2}\)
5.(\(\sqrt{8}-5\sqrt{2}+\sqrt{20}\)).\(\sqrt{5}\)+(40\(\sqrt{\frac{1}{10}}-10\)
6. \(\sqrt{2x}-3\sqrt{8x}+4\sqrt{18x}=14\)
Rút gọn:
a. \(\sqrt{7+2\sqrt{17\sqrt{2}}}-\sqrt{3\sqrt{2}+1}\)
b. \(\frac{\sqrt{20+8\sqrt{3}}+\sqrt{20-8\sqrt{3}}}{\sqrt{5+2\sqrt{3}}-\sqrt{5-2\sqrt{3}}}\) - \(\frac{\sqrt{4+\sqrt{3}}+\sqrt{4-\sqrt{3}}}{\sqrt{4+\sqrt{3}}-\sqrt{4-\sqrt{3}}}\)
