ta có: \(\left(4+\sqrt{15}\right)\sqrt{2\left(\sqrt{5}-\sqrt{3}\right)}\sqrt{4-\sqrt{15}}\)
\(=\left(4+\sqrt{15}\right)(\sqrt{5}-\sqrt{3})\sqrt{8-2\sqrt{3}.\sqrt{5}}\)
\(=\frac{\left(8+2\sqrt{15}\right)\left(\sqrt{5}-\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)}{2}\)
\(=\frac{\left(\sqrt{5}+\sqrt{3}\right)^2\left(\sqrt{5}-\sqrt{3}\right)^2}{2}\)
\(=\frac{\left(5-3\right)^2}{2}=2\)
Tính:
a) \(A=\left(\sqrt{6}+\sqrt{10}\right)-\sqrt{4-\sqrt{15}}\)
b) \(B=\left(3+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{2}\right).\sqrt{3-\sqrt{15}}\)
c) \(C=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\)
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\left(\sqrt{4-\sqrt{15}}\right)\)
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
Rút gọn biểu thức
a. \(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-\sqrt{12\sqrt{5}}}}}\)
b. \(B=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\left(\sqrt{4-\sqrt{15}}\right)\)
Cho A = \(\left(\frac{\sqrt{a}+1}{\sqrt{a}-1}-\frac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}-\frac{1}{\sqrt{a}}\right)\)
a) Rút gọn A
b) Tính A với a = \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
BT: Tính
a, \(\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\)
b,\(\left(3-\sqrt{5}\right)\cdot\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\cdot\sqrt{3-\sqrt{5}}\)
c,\(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
1. Rút gọn \(A=\sqrt{x+\sqrt{2x-1}}-\sqrt{x-\sqrt{2x-1}}\)
2. Tính \(B=\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}-\sqrt{3-2\sqrt{2}}\)
3.Tính \(C=\frac{\sqrt{3-\sqrt{5}}\cdot\left(\sqrt{10}-\sqrt{2}\right)\cdot\left(3+\sqrt{5}\right)}{\left(4+\sqrt{15}\right)\cdot\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}}\)
1) 2.\(\left(\sqrt{10}-\sqrt{2}\right).\)\(\sqrt{4+\sqrt{ }6-2\sqrt{5}}\)
2) \(\left(4\sqrt{2}+\sqrt{30}\right)\).\(\left(\sqrt{5}-\sqrt{3}\right)\)\(\sqrt{4-\sqrt{15}}\)
3) \(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
Gỉai giúp mk vs
\(\sqrt{21-6\sqrt{6}}\)
\(\sqrt{14-6\sqrt{5}}+\sqrt{14+6\sqrt{5}}\)
\(\left(3-\sqrt{2}\right)\sqrt{7+4\sqrt{3}}\)
\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
\(\sqrt{6}\left(\sqrt{26+15\sqrt{3}}+\sqrt{26-15\sqrt{3}}\right)\)
