Ta có: \(A=\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5+1}}}-\sqrt{3-2\sqrt{2}}\)
Do \(\left(\dfrac{\sqrt{\sqrt{5}+2}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}\right)^2=\dfrac{\left(\sqrt{5}+2\right)+2\sqrt{\left(\sqrt{5}+2\right)\left(\sqrt{5}-2\right)}+\left(\sqrt{5}-2\right)}{\sqrt{5}+1}\)\(=\dfrac{\sqrt{5}+2+2\sqrt{\left(5-4\right)}+\sqrt{5}-2}{\sqrt{5}+1}=\dfrac{2\sqrt{5}+2}{\sqrt{5}+1}=\dfrac{2\left(\sqrt{5}+1\right)}{\sqrt{5+1}}=2\)\(\Rightarrow\dfrac{\sqrt{\sqrt{5+2}}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+1}}=\sqrt{2}\)
Maf \(\sqrt{3-2\sqrt{2}}=\sqrt{2-2\sqrt{2}+1}=\sqrt{\left(\sqrt{2}-1\right)^2=\sqrt{2}-1}\)
\(\Rightarrow A=\sqrt{2}-\left(\sqrt{2}-1\right)=1\)
