Kết quả phép tính ​\(\begin{aligned} &\frac{2 \sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6-\sqrt{2}}} \end{aligned}\) là:

* Hướng dẫn giải

 \(\begin{aligned} &\frac{2 \sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6-\sqrt{2}}} \\ &=\frac{2 \sqrt{3-\sqrt{3+\sqrt{2 \sqrt{3}+1^{2}}}}}{\sqrt{6-\sqrt{2}}}=\frac{2 \sqrt{3-\sqrt{3+2 \sqrt{3}+1}}}{\sqrt{6}-\sqrt{2}} \\ &=\frac{2 \sqrt{3-\sqrt{\sqrt{3}+1^{2}}}}{\sqrt{6}-\sqrt{2}}=\frac{2 \sqrt{2-\sqrt{3}}}{\sqrt{6}-\sqrt{2}}=\frac{\sqrt{2} \sqrt{4-2 \sqrt{3}}}{\sqrt{2} \sqrt{3}-1}=1 \end{aligned}\)