\(A=\dfrac{2\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}}{\sqrt{10}-\sqrt{2}}=\dfrac{2\sqrt{4-\sqrt{5+\sqrt{20+4\sqrt{5}+1}}}}{\sqrt{10}-\sqrt{2}}\)\(=\dfrac{2\sqrt{4-\sqrt{5+\sqrt{\left(2\sqrt{5}+1\right)^2}}}}{\sqrt{10}-\sqrt{2}}=\dfrac{2\sqrt{4-\sqrt{5+\left(2\sqrt{5}+1\right)}}}{\sqrt{10}-\sqrt{2}}=\)\(=\dfrac{2\sqrt{4-\sqrt{\left(\sqrt{5}+1\right)^2}}}{\sqrt{10}-\sqrt{2}}=\dfrac{2\sqrt{4-\sqrt{5}-1}}{\sqrt{10}-\sqrt{2}}=\dfrac{\sqrt{2}.\sqrt{6-2\sqrt{5}}}{\sqrt{10}-\sqrt{2}}=\dfrac{\sqrt{2}.\sqrt{5-2\sqrt{5}+1}}{\sqrt{10}-\sqrt{2}}=\dfrac{\sqrt{2}.\sqrt{\left(\sqrt{5}-1\right)^2}}{\sqrt{10}-\sqrt{2}}=\dfrac{\sqrt{2}.\left(\sqrt{5}-1\right)}{\sqrt{10}-\sqrt{2}}=\dfrac{\sqrt{10}-\sqrt{2}}{\sqrt{10}-\sqrt{2}}=1\)
