Question

Answer 1

\(C=\sqrt{14-8\sqrt{3}}-\sqrt{21-12\sqrt{3}}\)

\(=\sqrt{2\left(7-4\sqrt{3}\right)}-\sqrt{12-2\cdot2\sqrt{3}\cdot3+9}\)

\(=\sqrt{2}\cdot\sqrt{4-2\cdot2\cdot\sqrt{3}+3}-\sqrt{\left(\sqrt{12}-3\right)^2}\)

\(=\sqrt{2}\cdot\sqrt{\left(2-\sqrt{3}\right)^2}-\left|2\sqrt{3}-3\right|\)

\(=\sqrt{2}\cdot\left|2-\sqrt{3}\right|-\left(2\sqrt{3}-3\right)\) (vì \(2\sqrt{3}-3>0\) )

\(=\sqrt{2}\cdot\left(2-\sqrt{3}\right)-2\sqrt{3}+3\) (vì \(2-\sqrt{3}>0\) )

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