\(\sqrt{18-2\sqrt{65}}\)
\(=\sqrt{\left(\sqrt{5}-\sqrt{13}\right)^2}\)
\(=\sqrt{13}-\sqrt{5}\)
\(\sqrt{18-2\sqrt{65}}\)
\(=\sqrt{\left(\sqrt{5}-\sqrt{13}\right)^2}\)
\(=\sqrt{13}-\sqrt{5}\)
\(\sqrt{6+2\sqrt{2}\sqrt{3+\sqrt{\sqrt{2}+\sqrt{12+\sqrt{18-\sqrt{18-\sqrt{128}}}}}}}\)
Tính:
E=(\(\sqrt{18}-3\sqrt{6}+\sqrt{2}\)) \(\sqrt{2}+6\sqrt{3}\)
G=\(\left(2\sqrt{2}-\sqrt{5}+\sqrt{18}\right)\).\(\left(\sqrt{50}+\sqrt{5}\right)\)
H=\(\dfrac{2+\sqrt{2}}{\sqrt{2}+1}\).\(\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)
Tính giá trị biểu thức:
\(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}-\sqrt{2}\)
\(\sqrt{9-2\sqrt{18}}+\sqrt{9+2\sqrt{18}}\)
Tính giá trị biểu thức : \(A=\sqrt{2+\sqrt[3]{3+\sqrt[4]{4+\sqrt[5]{5+...+\sqrt[14]{14+\sqrt[15]{15}}}}}}\)
rút gọn biểu thức sau
D=\(\left(\sqrt{x-\sqrt{18}}-\sqrt{x+\sqrt{18}}\right)\sqrt{x+\sqrt{x^2-18}}\) với \(x\ge18\)
A=\(\sqrt{x+6\sqrt{x-9}}+\sqrt{x-6\sqrt{x-9}}\)
C=\(\dfrac{\sqrt{2-\sqrt{2-4-x^2}}\left[\sqrt{\left(2+x\right)^3}+\sqrt{\left(2-x\right)^3}\right]}{4-\sqrt{4-x^2}}\)
\(\dfrac{\sqrt{2}-1}{\sqrt{2}+1}-\dfrac{3-\sqrt{2}}{3+\sqrt{2}}\)
\(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{3}{\sqrt{18}+2\sqrt{3}}\)
Tính
\(A=\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{\sqrt{2}+\sqrt{12+\sqrt{18}-\sqrt{128}}}}}\)
Tinhs \(\left(\sqrt{125}-\sqrt{18}-\sqrt{5}-\sqrt{2}\right)\left(\sqrt{125}+2\sqrt{8}-\sqrt{20}-\sqrt{2}\right)\)