Sửa đề : \(\sqrt[3]{6\sqrt{3}+10}-\sqrt[3]{6\sqrt{3}-10}\)
\(=\sqrt[3]{\left(\sqrt{3}+1\right)^3}-\sqrt[3]{\left(\sqrt{3}-1\right)^2}\)
\(=\sqrt{3}+1-\left(\sqrt{3}-1\right)=2\)
\(\left(\dfrac{\sqrt{6}-\sqrt{10}}{\sqrt{5}-\sqrt{3}}+3\right)\left(3+\dfrac{2\sqrt{5}+\sqrt{6}}{\sqrt{10}+\sqrt{3}}\right)\)
Rút gọn biểu thức trên
Tính :
\(A=\sqrt[3]{6\sqrt{3}+10}-\sqrt[3]{6\sqrt{3}-10}\)
\(B=\dfrac{4+2\sqrt{3}}{\sqrt[3]{10+6\sqrt{3}}}\)
\(C=\sqrt[4]{56-24\sqrt{5}}\)
a)\(\sqrt{3+\sqrt{3}+\sqrt[3]{10+6\sqrt{3}}}\)
b)\(\dfrac{4+2\sqrt{3}}{\sqrt[3]{10+6\sqrt{3}}}\)
\(\dfrac{2\sqrt{15}+2\sqrt{10}+\sqrt{6}-3}{2\sqrt{5}-2\sqrt{10}-\sqrt{3}+6}\)
Tính
a)B=\(\sqrt[3]{6\sqrt{3}+10}-\sqrt[3]{6\sqrt{3}-10}\)
b)C=\(\sqrt[3]{7+5\sqrt{2}}+\sqrt[3]{7-5\sqrt{2}}\)
\(\sqrt{10+2\sqrt{10}+2\sqrt{15}+2\sqrt{6}}\)
\(\left(3-\sqrt{2}\right)\sqrt{7+4\sqrt{3}}\)
1) \(\sqrt{7-2\sqrt{10}}\) - \(\sqrt{7+2\sqrt{10}}\)
2) \(\sqrt{4-2\sqrt{3}}\) + \(\sqrt{4+2\sqrt{3}}\)
3) \(\sqrt{6-4\sqrt{2}}\) + \(\sqrt{22-12\sqrt{2}}\)
Tính: ( Nhân cả tử lẫn mẫu với biểu thức liên hợp )
\(\dfrac{\sqrt{3}}{\sqrt{\sqrt{6}+}-1}-\dfrac{\sqrt{3}}{\sqrt{\sqrt{6}+1}+1}\)
\(\dfrac{2\sqrt{3}}{\sqrt{2}+\sqrt{3}+\sqrt{5}}+\dfrac{2}{\sqrt{6}+\sqrt{10}}\)
Bài 1: Tính
1, \(A=\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right).\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
2, \(B=\left(\frac{3\sqrt{125}}{15}-\frac{10-4\sqrt{6}}{\sqrt{5}-2}\right).\frac{1}{\sqrt{5}}\)
3, \(C=\left(\frac{\sqrt{1000}}{100}-\frac{5\sqrt{2}-2\sqrt{5}}{2\sqrt{5}-8}\right).\frac{\sqrt{10}}{10}\)
4, \(D=\frac{1}{\sqrt{49+20\sqrt{6}}}-\frac{1}{\sqrt{49-20\sqrt{6}}}+\frac{1}{\sqrt{7-4\sqrt{3}}}\)
5, \(E=\frac{1}{\sqrt{4-2\sqrt{3}}}-\frac{1}{\sqrt{7-\sqrt{48}}}+\frac{3}{\sqrt{14-6\sqrt{5}}}\)
6, \(F=\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)
7, \(G=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}-\sqrt{11-2\sqrt{10}}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}+\sqrt{12+8\sqrt{2}}}}\)
