Question

Tính:

\(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}-\sqrt{2}\right)\left(2+\sqrt{3}\right)\)

 

Answer 1

\(\sqrt{2-\sqrt{3}}\left(\sqrt{6}-\sqrt{2}\right)\left(2+\sqrt{3}\right)\)

\(=\sqrt{2-\sqrt{3}}\left(2\sqrt{6}+\sqrt{18}-2\sqrt{2}-\sqrt{6}\right)\)

\(=\sqrt{2-\sqrt{3}}\left(\sqrt{6}+\sqrt{2}\right)\) 

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

\(=\sqrt{\left(2-\sqrt{3}\right)\left(8+4\sqrt{3}\right)}\)

\(=\sqrt{16+8\sqrt{3}-8\sqrt{3}-12}\)

\(=\sqrt{16-12}\)

\(=\sqrt{4}\)

\(=2\)

Answer 2

Mong anh thịnh k trả lời ^^