Question

Thực hiện phép tính :

\(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)

Answer 1

\(\sqrt{3+\sqrt{5}}-\sqrt{3-\sqrt{5}}-\sqrt{2}\)

\(=\sqrt{\frac{6+2\sqrt{5}}{2}}-\sqrt{\frac{6-2\sqrt{5}}{2}}-\sqrt{2}\)

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

\(=\frac{2}{\sqrt{2}}-\sqrt{2}=0\)

Answer 2

bn chép lại đề nha

\(=\sqrt{6+2\sqrt{5}}+\sqrt{6-2\sqrt{5}}+2\)

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

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