Question

\(\sqrt{9+2\sqrt{20}}-\sqrt{9-2\sqrt{20}}\)

Answer 1

\(\sqrt{9+2\sqrt{20}}-\sqrt{9-2\sqrt{20}}=\sqrt{\left(\sqrt{5}+2\right)^2}-\sqrt{\left(\sqrt{5}-2\right)^2}=\left|\sqrt{5}+2\right|-\left|\sqrt{5}-2\right|=\sqrt{5}+2-\sqrt{5}+2=4\)

Answer 2

= \(\sqrt{\left(2+\sqrt{5}\right)^2}+\sqrt{\left(2-\sqrt{5}\right)^2}=2+\sqrt{5}+2-\sqrt{5}=4\)

Answer 3

\(\sqrt{9+2\sqrt{20}}-\sqrt{9-2\sqrt{20}}\)

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

=4