Question

Rút gọn : \(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

Answer 1

\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+\sqrt{16}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)=\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+2\sqrt{2}+2+2}{\sqrt{2}+\sqrt{3}+2}\)

=\(\frac{\sqrt{2}+\sqrt{3}+2}{\sqrt{2}+\sqrt{3}+2}+\frac{\sqrt{6}+2\sqrt{2}+2}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)=\(\frac{\sqrt{2}+\sqrt{3}+2}{\sqrt{2}+\sqrt{3}+2}+\frac{\sqrt{2}\left(\sqrt{3}+2+\sqrt{2}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

=1+\(\sqrt{2}\)