Question

Rút gọn biểu thức: \(\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

Answer 1

đặt: \(A=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\)

\(\Leftrightarrow A-1=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4}{\sqrt{2}+\sqrt{3}+\sqrt{4}}-1\\ \Leftrightarrow A-1=\dfrac{\sqrt{2}+\sqrt{3}+\sqrt{6}+\sqrt{8}+4-\sqrt{2}-\sqrt{3}-\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ \Leftrightarrow A-1=\dfrac{\sqrt{6}+\sqrt{8}+\sqrt{4}}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ \Leftrightarrow A-1=\dfrac{\sqrt{2}\left(\sqrt{2}+\sqrt{3}+\sqrt{4}\right)}{\sqrt{2}+\sqrt{3}+\sqrt{4}}\\ \Leftrightarrow A-1=\sqrt{2}\Rightarrow A=\sqrt{2}+1\)

Answer 2

Ahihi mấy bạn thật là thú dzị quá đi :v