Question

Tính giá trị biểu thức:

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

Answer 1

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

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

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

 

Answer 2

Ta có: \(\sqrt{\left(2-\sqrt{5}\right)^2}+\sqrt{\left(2\sqrt{2}-\sqrt{5}\right)^2}\)

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

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