\(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)
\(=\frac{\sqrt{2}.\sqrt{2-\sqrt{3}}}{\sqrt{2}}+\frac{\sqrt{2}.\sqrt{2+\sqrt{3}}}{\sqrt{2}}\)
\(=\frac{\sqrt{2.\left(2-\sqrt{3}\right)}}{\sqrt{2}}+\frac{\sqrt{2.\left(2+\sqrt{3}\right)}}{\sqrt{2}}\)
\(=\frac{\sqrt{4-2\sqrt{3}}}{\sqrt{2}}+\frac{\sqrt{4+2\sqrt{3}}}{\sqrt{3}}\)
\(=\frac{\sqrt{3-2\sqrt{3}+1}}{\sqrt{2}}+\frac{\sqrt{3+2\sqrt{3}+1}}{\sqrt{2}}\)
\(=\frac{\sqrt{\left(\sqrt{3}-1\right)^2}}{\sqrt{2}}+\frac{\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{2}}\)
\(=\frac{\left|\sqrt{3}-1\right|}{\sqrt{2}}+\frac{\left|\sqrt{3}+1\right|}{\sqrt{2}}\)
\(=\frac{\sqrt{3}-1}{\sqrt{2}}+\frac{\sqrt{3}+1}{\sqrt{2}}\)
\(=\frac{\sqrt{3}-1+\sqrt{3}+1}{\sqrt{2}}\)
\(=\frac{2\sqrt{3}}{\sqrt{2}}\)
\(=\frac{2\sqrt{3}.\sqrt{2}}{\left(\sqrt{2}\right)^2}\)
\(=\frac{2\sqrt{6}}{2}\)
\(=\sqrt{6}\)
Chúc bạn hok tốt!!! The Godlin
