Question

Thu gọn các biểu thức
\(A=\dfrac{2\left(\sqrt{2}+\sqrt{6}\right)}{3\sqrt{2+\sqrt{3}}}\)

\(B=\sqrt{8-2\sqrt{15}}-\sqrt{\left(3-3\sqrt{5}\right)^2}\)

\(C=2\sqrt{8\sqrt{3}}-2\sqrt{5\sqrt{3}}-3\sqrt{20-\sqrt{3}}\)

Answer 1

\(A=\dfrac{2\left(\sqrt{2}+\sqrt{6}\right)}{3\sqrt{2+\sqrt{3}}}=\dfrac{4\left(\sqrt{2}+\sqrt{6}\right)}{3.\sqrt{4\left(2+\sqrt{3}\right)}}=\dfrac{4\left(\sqrt{2}+\sqrt{6}\right)}{3.\sqrt{8+2\sqrt{12}}}=\dfrac{4\left(\sqrt{2}+\sqrt{6}\right)}{3.\sqrt{\left(\sqrt{2}+\sqrt{6}\right)^2}}=\dfrac{4}{3}\)

\(B=\sqrt{8-2\sqrt{15}}-\sqrt{\left(3-3\sqrt{5}\right)^2}=\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}-3\sqrt{5}+3\\ =\sqrt{5}-\sqrt{3}-3\sqrt{5}+3=3-\sqrt{3}-2\sqrt{5}\)