Question

Tính:

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

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

Làm tiếp ... 

Answer 1

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

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

\(=\sqrt{4-2\sqrt{3}}\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)\)

\(=\sqrt{\left(\sqrt{3}\right)^2-2\sqrt{3}\cdot1+1}\left(\sqrt{3}-1\right)\left(2+\sqrt{3}\right)\)

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

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

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

\(=8+4\sqrt{3}-4\sqrt{3}-6\)

\(=2\)