Question

Rút gọn

a) \(\frac{\sqrt{8-2\sqrt{12}}}{\sqrt{3}-1}-\sqrt{8}\)

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

Answer 1

\(A=\frac{\sqrt{\left(\sqrt{6}-\sqrt{2}\right)^2}}{\sqrt{3}-1}-2\sqrt{2}=\frac{\sqrt{6}-\sqrt{2}}{\sqrt{3}-1}-2\sqrt{2}=\frac{\sqrt{2}\left(\sqrt{3}-1\right)}{\sqrt{3}-1}-2\sqrt{2}=-\sqrt{2}\)

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

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

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