Cho x= \(\dfrac{\sqrt{13-4\sqrt{3}}}{2}.Tính\) A = \(\dfrac{\sqrt{x}+2}{2\sqrt{x}-3}\)
Rút gọn các biểu thức sau:
D = \(\sqrt{9+4\sqrt{2}}-3\)
E = \(\sqrt{4+2\sqrt{3}}-\sqrt{13+4\sqrt{3}}\)
F = \(\sqrt{7-4\sqrt{3}}+\sqrt{4-2\sqrt{3}}\)
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. (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.\(\sqrt{13-\sqrt{160\:\:\:\:}}\:+\:\sqrt{53+4\sqrt{90}}\)
\(\sqrt{13-\sqrt{160}}\) + \(\sqrt{53+4\sqrt{90}}\)
\(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
Tính
a) \(\sqrt{\left(4-2\sqrt{3}\right).\left(13+4\sqrt{3}\right)}\)
b) \(\left(\sqrt{3}-2\right).\left(\sqrt{6}+\sqrt{2}\right).\sqrt{\sqrt{3}+2}\)
c)\(\left(3+\sqrt{5}\right).\left(\sqrt{10}-\sqrt{2}\right).\sqrt{3-\sqrt{5}}\)
d) \(\left(4+\sqrt{15}\right).\left(\sqrt{10}-\sqrt{6}\right).\sqrt{4-\sqrt{15}}\)
Giúp mk với, mk hứa sẽ tick cho.Cảm ơn nhiều!!
Tính
a) \(\sqrt{13-4\sqrt{2}}\)
b) \(2\sqrt{40\sqrt{12}}-2\sqrt{75}-3\sqrt{5\sqrt{48}}\)
c) \(\sqrt{1+\dfrac{1}{1^2}+\dfrac{2}{2^2}}+\sqrt{1+\dfrac{1}{2^2}+\dfrac{2}{3^2}}+\sqrt{1+\dfrac{1}{3^2}+\dfrac{2}{4^2}}+...+\sqrt{1+\dfrac{1}{99^2}+\dfrac{2}{100^2}}\)
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)\(\sqrt{x-10}=-2\)