a: \(=\left(3-\sqrt{5}\right)\cdot\left(\sqrt{5}-1\right)\cdot\left(\sqrt{5}+1\right)\)
\(=4\left(3-\sqrt{5}\right)=12-4\sqrt{5}\)
b: \(=\left(4+\sqrt{15}\right)\cdot\left(\sqrt{5}-\sqrt{3}\right)^2\)
\(=\left(4+\sqrt{15}\right)\left(8-2\sqrt{15}\right)\)
\(=32-8\sqrt{15}+8\sqrt{15}-30\)
=2
\(\left(\sqrt{6}+\sqrt{10}\right).\sqrt{4-\sqrt{15}}\)
\(\left(3+\sqrt{15}\right).\left(\sqrt{10}-2\right).\sqrt{3-\sqrt{5}}\)
\(\left(4+\sqrt{15}\right).\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\)
\(a.\left(3-\sqrt{5}\right)\left(\sqrt{10}-2\right).\sqrt{3+\sqrt{5}}\\ \)
\(b.\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\\ \)
Rút gọn:
a)\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b)\(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
Tính :
a)\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b)\(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
c) \(\frac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}}+1}-\sqrt{3-2\sqrt{2}}\)
B1: rút gọn biểu thức:
a, \(\frac{\left(4\sqrt{21}-4\sqrt{15}-\sqrt{4}+\sqrt{10}\right)}{4\sqrt{6}-2+4\sqrt{15}-\sqrt{10}}\)
b, \(\left(\sqrt{5}+\sqrt{3}\right)\sqrt{8-2\sqrt{15}}\)
c, \(\sqrt{3-\sqrt{5}}-\sqrt{3+\sqrt{5}}\)
d, \(\left(2-\sqrt{3}\right)\left(\sqrt{6}+\sqrt{2}\right)\sqrt{2+\sqrt{3}}\)
Tính : \(A=\left(\sqrt{5}-\sqrt{2}\right)^{^2}+2\sqrt{10}\)
\(B=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\left(\sqrt{4}-\sqrt{15}\right)\)
\(C=\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\)
a)\(\sqrt{\left(2\sqrt{2}-3\right)^2+\sqrt{15}}\)
b)\(\sqrt{\left(\sqrt{10}-3\right)}^2+\sqrt{\left(\sqrt{10}-4\right)^2}\)
c)\(11+6\sqrt{2}=\left(3+\sqrt{2}\right)^2\)
d)\(\sqrt{11}+6\sqrt{2}+\sqrt{11-6\sqrt{2}=6}\)
CM các đẳng thức sau:
\(\sqrt{3-\sqrt{5}}(3+\sqrt{5})\left(\sqrt{10}-\sqrt{2}\right)=8\)
\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}=2}\)
Thực hiện phép tính ( rút gọn biểu thức )
a) \(\left(\sqrt{14}+\sqrt{6}\right)\sqrt{5-\sqrt{21}}\)
b) \(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\)\(\sqrt{4-\sqrt{15}}\)
Giup dum mik
Tính:
\(\left(3-\sqrt{5}\right)\sqrt{3+\sqrt{5}}+\left(3+\sqrt{5}\right)\sqrt{3-\sqrt{5}}\)\(\left(4+\sqrt{15}\right)\sqrt{4-\sqrt{15}}\left(\sqrt{10}-\sqrt{6}\right)\)
