Question

Rút gọn:

A = \(\sqrt{\dfrac{3\sqrt{3}-4}{2\sqrt{3}+1}}+\sqrt{\dfrac{\sqrt{3}+4}{5-2\sqrt{3}}}\)

Answer 1

ta có:

\(A^2=\dfrac{3\sqrt{3}-4}{2\sqrt{3}+1}+2\sqrt{\dfrac{\left(3\sqrt{3}-4\right)\left(\sqrt{3}+4\right)}{\left(2\sqrt{3}+1\right)\left(5-2\sqrt{3}\right)}}+\dfrac{\sqrt{3}+4}{5-2\sqrt{3}}\)

\(A^2=\dfrac{\left(3\sqrt{3}-4\right)\left(5-2\sqrt{3}\right)+\left(2\sqrt{3}+1\right)\left(\sqrt{3}+4\right)}{\left(2\sqrt{3}+1\right)\left(5-2\sqrt{3}\right)}+2\sqrt{\dfrac{9+12\sqrt{3}-4\sqrt{3}-16}{10\sqrt{3}-12+5-2\sqrt{3}}}\)

\(A^2=\dfrac{15\sqrt{3}-18-20+8\sqrt{3}+6+8\sqrt{3}+\sqrt{3}+4}{10\sqrt{3}-12+5-2\sqrt{3}}+2\sqrt{\dfrac{8\sqrt{3}-7}{8\sqrt{3}-7}}\)

\(A^2=\dfrac{32\sqrt{3}-28}{8\sqrt{3}-7}+2\)

\(A^2=6\Rightarrow a=\sqrt{6}\)