Đặt \(A=\sqrt{2-\sqrt{3}}\left(\sqrt{6}-\sqrt{2}\right)\left(2+\sqrt{3}\right)\)
\(=\dfrac{\sqrt{2}}{\sqrt{2}}\left(\sqrt{2-\sqrt{3}}\right)\left(\sqrt{6}-\sqrt{2}\right)\left(2+\sqrt{3}\right)\)
\(=\sqrt{2}\left(\sqrt{2-\sqrt{3}}\right)\left(\dfrac{\sqrt{6}-\sqrt{2}}{\sqrt{2}}\right)\left(2+\sqrt{3}\right)\)
\(=\sqrt{4-2\sqrt{3}}\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)\)
\(=\sqrt{\left(\sqrt{3}-1\right)^2}\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)\)
\(=\left(\sqrt{3}-1\right)\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)\)
\(=\left(3-2\sqrt{3}+1\right)\left(2+\sqrt{3}\right)\)
\(=6+3\sqrt{3}-4\sqrt{3}-6+2+\sqrt{4}\)
\(=2\)
Chúc bạn học tốt
