Question

Tính:( Các bạn bấm máy tính nhé)

1.\(\left(\sqrt{10}-\sqrt{14}\right).\left(\sqrt{6+\sqrt{35}}\right)\)

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

Answer 1

1: \(\left(\sqrt{10}-\sqrt{14}\right)\cdot\sqrt{6+\sqrt{35}}\)

\(=\left(\sqrt{5}-\sqrt{7}\right)\cdot\sqrt{12+2\sqrt{35}}\)

\(=\left(\sqrt{5}-\sqrt{7}\right)\left(\sqrt{5}+\sqrt{7}\right)\)

=5-7=-2

2: Sửa đề: \(\sqrt{4+\sqrt{8}}\cdot\sqrt{2+\sqrt{2+\sqrt{2}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2}}}\)

\(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{2^2-\left(2+\sqrt{2}\right)}\)

\(=\sqrt{4+2\sqrt{2}}\cdot\sqrt{4-2-\sqrt{2}}\)

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