Question

Tính:

A = \(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)

Answer 1

\(A=\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\\A= \sqrt{6-2\sqrt{5}}\left(\sqrt{5}-1\right)\left(3+\sqrt{5}\right)\\ A=\sqrt{\left(\sqrt{5}\right)^2-2\cdot\sqrt{5}\cdot1+1}\left(\sqrt{5}-1\right)\left(3+\sqrt{5}\right)\\ A=\sqrt{\left(\sqrt{5}-1\right)^2}\left(\sqrt{5}-1\right)\left(3+\sqrt{5}\right)\\ A=\left(\sqrt{5}-1\right)\left(\sqrt{5}-1\right)\left(3+\sqrt{5}\right)\\ A=\left(\sqrt{5}-1\right)^2\left(3+\sqrt{5}\right)\\ A=\left(6-2\sqrt{5}\right)\left(3+\sqrt{5}\right)=8\)