Question

Tính: \(A=\dfrac{\sqrt{6+2\left(\sqrt{6}+\sqrt{3}+\sqrt{2}\right)}-\sqrt{6-2\left(\sqrt{6}-\sqrt{3}+\sqrt{2}\right)}}{\sqrt{2}}\)

Answer 1

\(A=\dfrac{\sqrt{6+2\left(\sqrt{6}+\sqrt{3}+\sqrt{2}\right)}-\sqrt{6-2\left(\sqrt{6}-\sqrt{3}+\sqrt{2}\right)}}{\sqrt{2}}=\dfrac{\sqrt{3+2+1+2\sqrt{6}+2\sqrt{3}+2\sqrt{2}}-\sqrt{3+2+1-2\sqrt{6}+2\sqrt{3}-2\sqrt{2}}}{\sqrt{2}}=\dfrac{\sqrt{\left(\sqrt{3}+\sqrt{2}+1\right)^2}-\sqrt{\left(\sqrt{3}-\sqrt{2}+1\right)^2}}{\sqrt{2}}=\dfrac{\sqrt{3}+\sqrt{2}+1-\sqrt{3}+\sqrt{2}-1}{\sqrt{2}}=\dfrac{2\sqrt{2}}{\sqrt{2}}=2\)