Question

Rut gọn bt

 \(A=\frac{\sqrt{6+\sqrt{12}-\sqrt{8}-\sqrt{24}}}{\sqrt{2}+\sqrt{3}+1}\)

Answer 1

\(A=\frac{\sqrt{6+\sqrt{12}-\sqrt{8}-\sqrt{24}}}{\sqrt{2}+\sqrt{3}+1}\)

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

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

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

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