Question

Thực hiện phép tính:

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

\(\sqrt{2-\sqrt{3}}\left(\sqrt{6}+\sqrt{2}\right)\)

\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)

Answer 1

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

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

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

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

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

\(=\frac{\sqrt{5}-1+\sqrt{5}+1}{\sqrt{2}}=\frac{2\sqrt{5}}{\sqrt{2}}=\frac{\sqrt{2}.\sqrt{2}.\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)