Question

Giúp mình với mình cảm ơn trước!!! Rút gọn biểu thức nha:

\(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt[]{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)

Answer 1

\(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\\ =\sqrt{2\left(2+\sqrt{2}\right)}.\sqrt{\left(2+\sqrt{2+\sqrt{2}}\right)\left(2-\sqrt{2+\sqrt{2}}\right)}\\ =\sqrt{2}.\sqrt{2+\sqrt{2}}.\sqrt{4-\left(2+\sqrt{2}\right)}\\ =\sqrt{2}.\sqrt{2+\sqrt{2}}.\sqrt{2-\sqrt{2}}\\ =\sqrt{2}.\sqrt{\left(2+\sqrt{2}\right)\left(2-\sqrt{2}\right)}\\ =\sqrt{2}.\sqrt{4-2}\\ =2\)