Question

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

Mn ơi giúp mk với

Answer 1

Ta thấy \(4+2\sqrt{3}=3+2\sqrt{3}+1=\left(\sqrt{3}+1\right)^2\)

\(\Rightarrow\sqrt{4+2\sqrt{3}}=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\)

\(\Rightarrow2\sqrt{2}\sqrt{3-\sqrt{4+2\sqrt{3}}}=2\sqrt{6-2\left(\sqrt{3}+1\right)}\)\(=2\sqrt{6-2\sqrt{3}-2}=2\sqrt{4-2\sqrt{3}}\)

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

\(\Rightarrow\sqrt{6+2\sqrt{2}\sqrt{3-\sqrt{4+2\sqrt{3}}}}=\sqrt{6+2\sqrt{3}-2}\)\(=\sqrt{\left(\sqrt{3}+1\right)^2}=\sqrt{3}+1\)

Answer 2

Trình bày hơi xấu e thông cảm