Đặt \(x=\sqrt{5+\sqrt{19+2\sqrt{5}}}-\sqrt{5-\sqrt{19+2\sqrt{5}}}>0\)
\(x^2=10-2\sqrt{\left(5+\sqrt{19+2\sqrt{5}}\right)\left(5-\sqrt{19+2\sqrt{5}}\right)}\)
\(x^2=10-2\sqrt{6-2\sqrt{5}}\)
\(x^2=10-2\sqrt{\left(\sqrt{5}-1\right)^2}\)
\(x^2=10-2\sqrt{5}+2\)
\(x^2=12-2\sqrt{5}\)
\(\Rightarrow x=\sqrt{12-2\sqrt{5}}\)
Tình
A= \(\dfrac{\sqrt{9+\sqrt{5}}+\sqrt{9-\sqrt{5}}}{\sqrt{9+ 2\sqrt{19}}}-\sqrt{3-2\sqrt{2}}\)
1. Tính ( rút gọn)
a)\(\sqrt{\left(5-\sqrt{19}\right)^2}-\sqrt{\left(4-\sqrt{19}\right)^2}\)
b)\(\sqrt{\left(3-2\sqrt{2}\right)^2}-\sqrt{\left(2\sqrt{2}-3\right)^2}\)
c)\(\sqrt{8+2\sqrt{15}}+\sqrt{\left(\sqrt{2-\sqrt{5}}\right)^2}\)
d)\(\sqrt{12+6\sqrt{3}}.\left(3+\sqrt{3}\right)\)
e) \(\left(2-\sqrt{5}\right).\sqrt{9+4\sqrt{5}}\)
\(\frac{\sqrt{5+2\sqrt{9\sqrt{5}-19}}-\sqrt{7-\sqrt{5}}}{2\sqrt{\sqrt{5}-2}}\)
Rút gọn:
A= \(\sqrt{6-2\sqrt{5}}\) C= \(\sqrt{19-8\sqrt{3}}\)
B = \(\sqrt{4-\sqrt{12}}\) D= \(\sqrt{5-2\sqrt{6}}\)
a : \(\sqrt{\left(2\sqrt{2}-1\right)^2}-\sqrt{17+12\sqrt{2}}\)
b : \(\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{14-6\sqrt{5}}\)
c : \(\sqrt{\left(4-3\sqrt{2}\right)^2}-\sqrt{19+6\sqrt{2}}\)
RÚT GỌN BIỂU THỨC
A=\(4-\sqrt{21-8\sqrt{5}}\)
B=\(\sqrt{4-2\sqrt{3}+1}\)
C=\(\sqrt{8+2\sqrt{15}}-\sqrt{5-2\sqrt{6}}\)
D=\(\sqrt{28-10\sqrt{3}}+\sqrt{4+2\sqrt{3}}\)
E=\(\sqrt{14-6\sqrt{5}}-\sqrt{21-8\sqrt{5}}\)
F=\(\sqrt{19-2\sqrt{40}}-\sqrt{19+3\sqrt{40}}\)
Tính
a) A = \(^{\sqrt[3]{5\sqrt{2}+7}-\sqrt[3]{5\sqrt{2}-7}+\sqrt{10+\sqrt{19}}-\sqrt{10-\sqrt{19}}}\) b) B = \(\frac{\sqrt{45+27\sqrt{2}}+\sqrt{45-27\sqrt{2}}}{\sqrt{5+3\sqrt{2}}-\sqrt{5-3\sqrt{2}}}-\frac{\sqrt{3+\sqrt{2}}+\sqrt{3-\sqrt{2}}}{\sqrt{3+\sqrt{2}-\sqrt{3-\sqrt{2}}}}\)
40.A=\(\dfrac{2-5\sqrt{x}}{\sqrt{x}+1}\)
a. Tính giá trị của biểu thức A khi x=\(\sqrt{19+8\sqrt{3}}+\sqrt{19-8\sqrt{3}}\)
Rút gọn:
a) \(\sqrt{15-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)
b) \(\sqrt{\left(3+\sqrt{5}\right)^2}+\sqrt{14-6\sqrt{5}}\)
c) \(\dfrac{3}{2\sqrt{3}+3}+\dfrac{3}{2\sqrt{3}-3}\)
d) \(\sqrt{\left(\sqrt{3}+4\right)\sqrt{19-8\sqrt{3}}+3}\)
e) \(\dfrac{9-2\sqrt{3}}{3\sqrt{6}-2\sqrt{2}}+\dfrac{3}{3+\sqrt{6}}\)
