Question

Answer 1

\(A=\sqrt{5-2\sqrt{6}}-\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}\)

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

\(=0\)

Answer 2

\(A=\sqrt{5-2\sqrt{6}}-\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}=\sqrt{\left(\sqrt{3}-\sqrt{2}\right)^2}-\left|\sqrt{2}-\sqrt{3}\right|=\left|\sqrt{3}-\sqrt{2}\right|+\sqrt{2}-\sqrt{3}=\sqrt{3}-\sqrt{2}+\sqrt{2}-\sqrt{3}=0\)

Answer 3

\(A=\sqrt{5-2\sqrt{6}}-\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}\)

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

=0