Question

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

Answer 1

=căn 4-2căn 3+2-căn 3

=căn 3-1+2-căn 3

=1

Answer 2

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

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

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

\(=\sqrt{3}-1+2-\sqrt{3}\) ( vì \(\sqrt{3}-1>0\) )

`=1`