Question

Rút gọn: A\(=\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)

Answer 1

\(A=\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\)

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

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

\(A^2=4+2\sqrt{4-3}\)

\(A^2=6\)

Vì \(A>0\)\(\Rightarrow A=\sqrt{6}\)

Answer 2

\(A=\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\\ A=\frac{\sqrt{2}\left(\sqrt{2-\sqrt{3}}+\sqrt{2+\sqrt{3}}\right)}{\sqrt{2}}\\ A=\frac{\sqrt{4-2\sqrt{3}}+\sqrt{4+2\sqrt{3}}}{\sqrt{2}}\\ A=\frac{\sqrt{\left(\sqrt{3}-1\right)^2}+\sqrt{\left(\sqrt{3}+1\right)^2}}{\sqrt{2}}\\ A=\frac{\sqrt{3}-1+\sqrt{3}+1}{\sqrt{2}}\\ A=\frac{2\sqrt{3}}{\sqrt{2}}\\ A=\sqrt{6}\)