Question

rút gọn

\(A=\dfrac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)

Answer 1

ta có :\(A=\dfrac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}=\dfrac{2\sqrt{3-\sqrt{3+\sqrt{13+4\sqrt{3}}}}}{\sqrt{6}-\sqrt{2}}\)

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

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

Answer 2

1