Question

Rút gọn biểu thức

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

b. \(B=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\left(\sqrt{4-\sqrt{15}}\right)\)

Answer 1

Phần a sai đề sửa đề

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

=\(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{(2\sqrt{5}-3)^2 } } } \)

=\(\sqrt{5-\sqrt{3-2\sqrt{5}+3 }}\)

=\(\sqrt{\sqrt{5}-\sqrt{(\sqrt{5}-1)^2 } } \)

=\(\sqrt{\sqrt{5}-\sqrt{5}+1 } \)

=1

Answer 2

B=\((\sqrt{4+\sqrt{15} }) \sqrt{2}(\sqrt{5}-\sqrt{3})(\sqrt{4-\sqrt{15} })({\sqrt{4+\sqrt{15} }) } \)

=(\((\sqrt{4+\sqrt{15} })\sqrt{2}(\sqrt{5}-\sqrt{3}) \)

=\((\sqrt{8+2\sqrt{15} })(\sqrt{5}-\sqrt{3}) \)

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

=2