Question

Thực hiện phép tính:

a) ( \(4+\sqrt{15}\))\(\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)

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

c) \(\left(\sqrt{3}-\sqrt{2}+1\right)\left(\sqrt{3}-1\right)\)

d) \(\sqrt{2+\sqrt{3}}.\sqrt{2+\sqrt{2+\sqrt{3}}}.\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}.\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)

Answer 1

\(\left(\sqrt{4+\sqrt{15}}\right)^2\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\sqrt{4-\sqrt{15}}=\left(\sqrt{4+\sqrt{15}}\sqrt{4-\sqrt{15}}\right)\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)\sqrt{4+\sqrt{15}}=\sqrt{8+2\sqrt{15}}\left(\sqrt{5}-\sqrt{3}\right)=\left(\sqrt{5}+\sqrt{3}\right)\left(\sqrt{5}-\sqrt{3}\right)=2\)