Question

Rút gọn các biểu thức :

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

\(b,\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\)

Answer 1

a/

\(=\frac{\sqrt{6+2\sqrt{5}}}{\sqrt{2}}+\frac{\sqrt{6-2\sqrt{5}}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}}{\sqrt{2}}=\frac{\sqrt{5}+1+\sqrt{5}-1}{\sqrt{2}}=\frac{2\sqrt{5}}{\sqrt{2}}=\sqrt{10}\)

b/

\(=\frac{\sqrt{8-2\sqrt{7}}}{\sqrt{2}}-\frac{\sqrt{8+2\sqrt{7}}}{\sqrt{2}}=\frac{\sqrt{\left(\sqrt{7}-1\right)^2}-\sqrt{\left(\sqrt{7}+1\right)^2}}{\sqrt{2}}=\frac{\sqrt{7}-1-\sqrt{7}-1}{\sqrt{2}}=\frac{-2}{\sqrt{2}}=-\sqrt{2}\)