Question

giải giúp mik vs

A=\(\sqrt{4-2\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)

B=\(\sqrt{3+\sqrt{8}+\sqrt{3-\sqrt{8}}}\)

Answer 1

Ta có : \(A=\sqrt{4-2\sqrt{3}}+\sqrt{7-4\sqrt{3}}\)

\(=\sqrt{3-2\sqrt{3}+1}+\sqrt{2^2-2.2\sqrt{3}+3}\)

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

\(=\sqrt{3}-1+2-\sqrt{3}=1\)

Ta có : \(B=\sqrt{3+\sqrt{8}+\sqrt{3-\sqrt{8}}}\)

\(=\sqrt{3+\sqrt{8}+\sqrt{2-2\sqrt{2}+1}}\)\(=\sqrt{3+\sqrt{8}+\sqrt{\left(\sqrt{2}-1\right)^2}}\)

\(=\sqrt{3+2\sqrt{2}+\sqrt{2}-1}\) \(=\sqrt{2+3\sqrt{2}}\)