Ta có : \(\sqrt{6-4\sqrt{2}}=\sqrt{\left(2\right)^2-2.2\sqrt{2}+\left(\sqrt{2}\right)^2}=\sqrt{\left(2-\sqrt{2}\right)^2}=\left|2-\sqrt{2}\right|=2-\sqrt{2}\)
thực hiện phép tính
A=\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2-\sqrt{2-\sqrt{3}}}}\)
B=\(\dfrac{6+4\sqrt{2}}{\sqrt{2+\sqrt{6+4\sqrt{2}}}}+\dfrac{6-4\sqrt{2}}{\sqrt{2}-\sqrt{6-4\sqrt{2}}}\)
\(\sqrt{5-2\sqrt{2+\sqrt{9+4\sqrt{2}}}}\sqrt{\sqrt{3-\sqrt{4-\sqrt{2-\sqrt{6-4\sqrt{10-4\sqrt{6}}}}}}}\)
thực hiện phép tính
A=\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
B=\(\left(5+2\sqrt{6}\right)\cdot\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}\)
Bài 1:
1.\(\sqrt{2-\sqrt{3}}\)
2.\(\sqrt{3+\sqrt{5}}\)
3.\(\sqrt{21-6\sqrt{6}}\)
4.\(\sqrt{5+2\sqrt{6}}-\sqrt{5-2\sqrt{6}}\)
5.\(\left(2-\sqrt{3}\right)\sqrt{7+4\sqrt{3}}\)
6.\(\sqrt{13+4\sqrt{10}}+\sqrt{13-4\sqrt{10}}\)
\(\left(5+4\sqrt{2}\right)\left(3+2\sqrt{1+\sqrt{2}}\right)\left(3-2\sqrt{1+\sqrt{2}}\right)\\ \\ \\ \sqrt{\frac{9}{4}-\sqrt{2}}\\ \\ \\ Sosanh2\sqrt{27}va\sqrt{147}\\ \\ \\ 2\sqrt{15}va\sqrt{59}\\ \\ \\ 2\sqrt{2}-1va2\\ \\ \\ \frac{\sqrt{3}}{2}va1\\ \\ \\ -\frac{\sqrt{10}}{2}va-2\sqrt{5}\\ \\ \\ \sqrt{6}-1va3\\ \\ \\ 2\sqrt{5}-5\sqrt{2}va1\\ \\ \\ \frac{\sqrt{8}}{3}va\frac{3}{4}\\ \\ \\ -2\sqrt{6}va-\sqrt{23}\\ \\ \\ 2\sqrt{6}-2va3\\ \\ \\ \sqrt{111}-7va4\)
Xếp theo thứ tự tăng dần: \(21,2\sqrt{7},15\sqrt{3},-\sqrt{123}\) ; \(28\sqrt{2},\sqrt{14},2\sqrt{147},36\sqrt{4}\)
giảm dần: \(6\sqrt{\frac{1}{4}},4\sqrt{\frac{1}{2}},-\sqrt{132},2\sqrt{3},\sqrt{\frac{15}{5}}\); \(-27,4\sqrt{3},16\sqrt{5},21\sqrt{2}\)
a)\(\frac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}-\frac{6\sqrt{2}-4}{3-\sqrt{2}}\)
b)\(\sqrt{2-\sqrt{3}}-\sqrt{\frac{3}{2}}\)
c)\(\frac{\sqrt{30}-\sqrt{2}}{\sqrt{8-\sqrt{15}}}-\sqrt{8-\sqrt{49+8\sqrt{3}}}\)
d) \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
e)\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
f)\(\frac{\left(5+2\sqrt{6}\right)\left(49-20\sqrt{6}\right)\sqrt{5-2\sqrt{6}}}{9\sqrt{3}-11\sqrt{2}}\)
g)\(\frac{\frac{\sqrt{2+\sqrt{3}}}{2}}{\frac{\sqrt{2+\sqrt{3}}}{2}-\frac{2}{\sqrt{6}}+\frac{\sqrt{2+\sqrt{3}}}{2\sqrt{3}}}\)
Tính:
a) \(\dfrac{\sqrt{7}-5}{2}-\dfrac{6-2\sqrt{7}}{4}+\dfrac{6}{\sqrt{7}-2}-\dfrac{5}{4+\sqrt{7}}\)
b) \(\dfrac{2}{\sqrt{6}-2}+\dfrac{2}{\sqrt{6}+2}+\dfrac{5}{\sqrt{6}}\)
c) \(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)
d) \(\dfrac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)
a.\(\sqrt{15+6\sqrt{6}}\)
b.\(\sqrt{17-12\sqrt{2}}+\sqrt{17+12\sqrt{2}}\)
c. \(\sqrt{3-2\sqrt{2}}+\sqrt{4-2\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)
A=\(\sqrt{19-3\sqrt{ }40}\)-\(\sqrt{19+3\sqrt{ }40}\)
B=\(\sqrt{21-6\sqrt{ }6}\) +\(\sqrt{9+2\sqrt{ }18}\) -2\(\sqrt{6+3\sqrt{ }3}\)
C=\(\sqrt{6+2\sqrt{ }2\sqrt{ }3-\sqrt{ }4+2\sqrt{ }3}\)
D=\(\sqrt{4+\sqrt{ }15}\)-\(\sqrt{7-3\sqrt{ }5}\)
E=\(\sqrt{2+\sqrt{ }3}\)+\(\sqrt{2-\sqrt{ }3}\)
F=\(\sqrt{12-3\sqrt{ }7}\)-\(\sqrt{12+3\sqrt{ }7}\)
G=(3\(\sqrt{2}\)+\(\sqrt{6}\)).\(\sqrt{6-3\sqrt{ }3}\)
H=\(\sqrt{9-4\sqrt{ }5}-\sqrt{14-6\sqrt{ }5}\)
I=\(\sqrt{9-4\sqrt{ }2}\)-\(\sqrt{13-4\sqrt{ }3}\)
a) \(\sqrt{13-4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)
b) \(\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}\)
c) \(\sqrt{4+2\sqrt{3}}-\sqrt{4-2\sqrt{3}}\)
d) \(\sqrt{7+4\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)
e) \(\sqrt{9+4\sqrt{5}}\)
f) \(\sqrt{23+8\sqrt{7}}\)
