Question

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

2.\(\sqrt{\left(\sqrt{7-2\sqrt{2}}\right)^2}+\sqrt{\left(3-2\sqrt{2}\right)^2}\)

Answer 1

Làm :

\(1.\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}\)

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

\(=\sqrt{5}-2+2\sqrt{2}-\sqrt{5}\) (\(do\left\{{}\begin{matrix}2< \sqrt{5}\\2\sqrt{2}=\sqrt{8}>\sqrt{5}\end{matrix}\right.\))

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

Kl:.....

\(2.\sqrt{\left(\sqrt{7-2\sqrt{2}}\right)^2}+\sqrt{\left(3-2\sqrt{2}\right)^2}\)

\(=\left|\sqrt{7-2\sqrt{2}}\right|+\left|3-2\sqrt{2}\right|\)

\(=\sqrt{7-2\sqrt{2}}+3-2\sqrt{2}\)

\(\approx5,1-2\sqrt{2}\)