Question

Chứng minh

\(\left(\sqrt{4}-\sqrt{3}\right)^2=\sqrt{49}-\sqrt{48}\)

\(2\sqrt{2}\left(2-3\sqrt{3}\right)+\left(1-2\sqrt{2}\right)^2+6\sqrt{6}=9\)

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

Answer 1

+) \(\left(\sqrt{4}-\sqrt{3}\right)^2=4-2\sqrt{4\cdot3}+3=7-2\sqrt{7}=\sqrt{49}-\sqrt{48}\)

+) \(2\sqrt{2}\left(2-3\sqrt{3}\right)+\left(1-2\sqrt{2}\right)^2+6\sqrt{6}\)

\(=4\sqrt{2}-6\sqrt{6}+9-4\sqrt{2}+6\sqrt{6}\)

\(=9\)

+) Sửa : \(\sqrt{8-2\sqrt{15}}-\sqrt{8+2\sqrt{15}}\)

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

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

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

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