Question

Từ \(6-2\sqrt{5}=\left(\sqrt{5}-1\right)^2\) rút gọn
\(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)

Answer 1

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

Answer 2

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

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

\(=\sqrt{5}+1-\sqrt{5}+1\left[Vì\left(\sqrt{5}+1\text{và}\sqrt{5}-1>0\right)\right]\)

\(=2\)