Question

Rút gọn:

\(\sqrt{7-2\sqrt{10}}+\sqrt{7+2\sqrt{10}}\)

Answer 1

\(\sqrt{7-2\sqrt{10}}+\sqrt{7+2\sqrt{10}}\)

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

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

\(=2\sqrt{5}\)

Answer 2

\(=\sqrt{5-2\sqrt{10}+2}+\sqrt{5+2\sqrt{10}+2}\\ =\sqrt{\left(\sqrt{5}-\sqrt{2}\right)^2}+\sqrt{\left(\sqrt{5}+\sqrt{2}\right)^2}\\ =\sqrt{5}-\sqrt{2}+\sqrt{5}+\sqrt{2}\\ =2\sqrt{5}\)