Question

\(\sqrt{\left(2\sqrt{5}-5\right)^2}+\sqrt{24-8\sqrt{5}}\)

Answer 1

\(\sqrt{\left(2\sqrt{5}-5\right)^2}+\sqrt{24-8\sqrt{5}}=\left|2\sqrt{5}-5\right|+\sqrt{\left(2\sqrt{5}-2\right)^2}=5-2\sqrt{5}+\left|2\sqrt{5}-2\right|=5-2\sqrt{5}+2\sqrt{5}-2=3\)

Answer 2

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

\(=5-2\sqrt{5}+2\sqrt{5}-2=5-2=3\)

Answer 3

\(\sqrt{\left(2\sqrt{5}-5\right)^2}+\sqrt{24-8\sqrt{5}}\)

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

\(=5-2\sqrt{5}+2\sqrt{5}-2=3\)

Answer 4

\(\sqrt{\left(2\sqrt{5}-5\right)^2}+\sqrt{24-8\sqrt{5}}\)

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

=3