Question

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

Answer 1

\(=\sqrt{\left(\sqrt{5}-1\right)^2}-\left|2-\sqrt{5}\right|=\left|\sqrt{5}-1\right|-\left|2-\sqrt{5}\right|\)

\(=\sqrt{5}-1-\sqrt{5}+2=1\)

Answer 2

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

\(=\sqrt{5}-1-\left(\sqrt{5}-2\right)\)

=-1+2

=1