\(=\sqrt{6+2\sqrt{5-\sqrt{\left(2\sqrt{3}+1\right)^2}}}\)
\(=\sqrt{6+2\sqrt{5-2\sqrt{3}-1}}\)
\(=\sqrt{6+2\left(\sqrt{3}-1\right)}=\sqrt{4+2\sqrt{3}}=\sqrt{3}+1\)
Rút gọn biểu thức:
a) \(\sqrt{6+2\sqrt{4-2\sqrt{3}}}\)
b) \(\sqrt{6-2\sqrt{3+\sqrt{13+4\sqrt{3}}}}\)
c) \(\sqrt{\sqrt{3}+\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)
d) \(\sqrt{23-6\sqrt{10+4\sqrt{3-2\sqrt{2}}}}\)
Rút gọn biểu thức
a)\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)
b)\(\sqrt{10+2\sqrt{17-4\sqrt{9+4\sqrt{5}}}}\)
Tìm x, biết
a)\(\sqrt{x-5}=3\)
b)\(\sqrt{x-10}=-2\)
\(\sqrt{5-\sqrt{13}+\sqrt{48}}\)
I.
1, \(\sqrt{8}-3\sqrt{32}+\sqrt{72}\)
2, \(6\sqrt{12}-2\sqrt{48}+5\sqrt{75}-7\sqrt{108}\)
3, \(\sqrt{20}+3\sqrt{45}-6\sqrt{80}-\dfrac{1}{3}\sqrt{125}\)
4, \(2\sqrt{5}-\sqrt{125}-\sqrt{80}\)
5, \(3\sqrt{2}-\sqrt{8}+\sqrt{50}-4\sqrt{32}\)
Rút gọn biểu thức
A. (2-√3)\(\sqrt{7+4\sqrt{3}}\)
B. \(\sqrt{13+4\sqrt{10}}\:+\:\sqrt[]{13-4\sqrt{10}}\)
C.(3 - √2) \(\sqrt{11+6\sqrt{2}}\)
D. (√5+√7) \(\sqrt{12-2\sqrt{35}}\)
E. (√2-√9)\(\sqrt{11+2\sqrt{18}}\)
F. \(\sqrt{46-6\sqrt{5}}\:+\:\sqrt{29-12\sqrt{5}}\)
G.\(\sqrt{49-5\sqrt{96}}\:+\:\sqrt{49+5\sqrt{96}}\)
H.\(\sqrt{13-\sqrt{160\:\:\:\:}}\:+\:\sqrt{53+4\sqrt{90}}\)
Tính :
a) A= \(\sqrt{\sqrt{3}+\sqrt{2}}.\sqrt{\sqrt{3}-\sqrt{2}}\)
b) B=\(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}\)
c) C= \(3-\sqrt{3-\sqrt{5}}\)
tính
1/ \(\sqrt{1,6}.\sqrt{30}.\sqrt{48}\)
2/ \(\frac{\sqrt{2}}{\sqrt{50}}\)
3/ \(\frac{\sqrt{6^5}}{\sqrt{2^3.3^5}}\)
4/ \(\sqrt{1\frac{9}{6}.5\frac{4}{9}.0,01}\)
1] rút gọn
a) (\(\sqrt{12}\) + \(3\sqrt{5}\) - \(4\sqrt{135}\)) 13
b) \(\sqrt{252}\) - \(\sqrt{700}\) + \(\sqrt{1008}\) - \(\sqrt{448}\)
c) \(2\sqrt{40\sqrt{12}}\) - \(2\sqrt{\sqrt{75}}\) -\(3\sqrt{5\sqrt{48}}\)
2]
a) A= \(\frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)
b) B= \(\frac{9\sqrt{5}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}\)
c) C= \(\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)
Tính
a) \(\sqrt{13-4\sqrt{2}}\)
b) \(2\sqrt{40\sqrt{12}}-2\sqrt{75}-3\sqrt{5\sqrt{48}}\)
c) \(\sqrt{1+\dfrac{1}{1^2}+\dfrac{2}{2^2}}+\sqrt{1+\dfrac{1}{2^2}+\dfrac{2}{3^2}}+\sqrt{1+\dfrac{1}{3^2}+\dfrac{2}{4^2}}+...+\sqrt{1+\dfrac{1}{99^2}+\dfrac{2}{100^2}}\)
A)\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
B)\(\left(\sqrt{2}+1^{ }\right)^3-\left(\sqrt{2}-1\right)^3\) C)\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\) D)\(\sqrt{\dfrac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\dfrac{2+\sqrt{3}}{2-\sqrt{3}}}\) E)\(\dfrac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\) F)\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{1}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
