Question

rút gọn:\(A=\dfrac{4\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}}{\sqrt{10}-\sqrt{2}}\)

Answer 1

\(A=\dfrac{4\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}}{\sqrt{10}-\sqrt{2}}=\dfrac{4\sqrt{4-\sqrt{5+\sqrt{\left(\sqrt{20}+1\right)^2}}}}{\sqrt{10}-\sqrt{2}}\\ =\dfrac{4\sqrt{4-\sqrt{\left(\sqrt{5}+1\right)^2}}}{\sqrt{10}-\sqrt{2}}=\dfrac{4\sqrt{3-\sqrt{5}}}{\sqrt{10}-\sqrt{2}}\\ =\dfrac{2\sqrt{\left(\sqrt{10}-\sqrt{2}\right)^2}}{\sqrt{10}-\sqrt{2}}=\dfrac{2\left(\sqrt{10}-\sqrt{2}\right)}{\sqrt{10}-\sqrt{2}}\\ =2\)