Question

Tính :

\(\sqrt{6+\sqrt{11}}-\sqrt{6-\sqrt{11}}+3\sqrt{2}\)

Answer 1

\(\sqrt{6+\sqrt{11}}+\sqrt{6-\sqrt{11}}+3\sqrt{2}\)

\(=\frac{\sqrt{12+2\sqrt{11}}}{\sqrt{2}}+\frac{\sqrt{12-2\sqrt{11}}}{\sqrt{2}}+3\sqrt{2}\)

\(=\frac{\sqrt{\left(\sqrt{11}+1\right)^2}}{\sqrt{2}}+\frac{\sqrt{\left(\sqrt{11}-1\right)^2}}{\sqrt{2}}+3\sqrt{2}\)

\(=\frac{\sqrt{11}+1}{\sqrt{2}}+\frac{\sqrt{11}-1}{\sqrt{2}}+3\sqrt{2}\)

\(=\frac{2\sqrt{11}}{\sqrt{2}}+3\sqrt{2}=\sqrt{22}+3\sqrt{2}\)