Question

\(\sqrt{13+4\sqrt{10}}\)

Answer 1

\(\sqrt{13+4\sqrt{10}}=\sqrt{8+2.2.\sqrt{2.5}+5}\)

\(=\sqrt{\left(2\sqrt{2}\right)^2+2.2\sqrt{2.5}+\left(\sqrt{5}\right)^2}\)

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

Answer 2

\(\sqrt{13+4\sqrt{10}}=\sqrt{8+2.2\sqrt{2}.\sqrt{5}+5}=\sqrt{\left(2\sqrt{2}+\sqrt{5}\right)^2}=2\sqrt{2}+\sqrt{5}\)

Answer 3

\(\sqrt{13+4\sqrt{10}}=\sqrt{8+2.2\sqrt{2}.\sqrt{5}+5}=\sqrt{\left(2\sqrt{2}+\sqrt{5}\right)^2}=\left|2\sqrt{2}+\sqrt{5}\right|=2\sqrt{2}+\sqrt{5}\)