Question

Tính giá trị các biểu thức sau:

a) \(A=\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

b) \(A=\sqrt[3]{8-\sqrt{60}}+\sqrt[3]{8+\sqrt{60}}\)

c) \(A=\frac{2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}}{\sqrt{6}+\sqrt{2}}\)

Answer 1

\(A=\sqrt{\sqrt{5}-\sqrt{3-\left(2\sqrt{5}-3\right)}}\)

\(=\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\)

\(=\sqrt{\sqrt{5}-\left(\sqrt{5}-1\right)}=\sqrt{1}=1\)

\(A=\sqrt[3]{8-\sqrt{60}}+\sqrt[3]{8+\sqrt{60}}\) xem lại đề con này

\(A=\frac{2\sqrt{3+\sqrt{5-\left(2\sqrt{3}+1\right)}}}{\sqrt{6}+\sqrt{2}}=\frac{2\sqrt{3+\sqrt{4-2\sqrt{3}}}}{\sqrt{6}+\sqrt{2}}=\frac{2\sqrt{3+\sqrt{3}-1}}{\sqrt{6}+\sqrt{2}}\)

\(=\frac{2\sqrt{4+2\sqrt{3}}}{2\left(\sqrt{3}+1\right)}=\frac{\sqrt{3}+1}{\sqrt{3}+1}=1\)