`(sqrt2+sqrt3+sqrt6+sqrt8+4)/(sqrt2+sqrt3+sqrt4)`
`=(sqrt2+sqrt3+2+2+sqrt6+sqrt8)/(sqrt2+sqrt3+sqrt4)`
`=(sqrt2+sqrt3+sqrt4+sqrt2(sqrt2+sqrt3+sqrt4))/(sqrt2+sqrt3+sqrt4)`
`=((sqrt2+sqrt3+sqrt4)(sqrt2+1))/(sqrt2+sqrt3+sqrt4)=sqrt2+1`
Lời giải:
\(\frac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{\sqrt{2}+\sqrt{3}+\sqrt{4}+\sqrt{4}+\sqrt{6}+\sqrt{8}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)
\(=\frac{(\sqrt{2}+\sqrt{3}+\sqrt{4})+\sqrt{2}(\sqrt{2}+\sqrt{3}+\sqrt{4})}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\frac{(\sqrt{2}+1)(\sqrt{2}+\sqrt{3}+\sqrt{4})}{\sqrt{2}+\sqrt{3}+\sqrt{4}}=\sqrt{2}+1\)
