c) C = căn bậc hai 3 căn bậc hai 3 - 4/ 2 căn bậc hai 3 + 1 - căn bậc hai căn bậc hai 3 + 4/ 5 - 2 căn bậc hai 3

* Hướng dẫn giải

c) $\mathrm{C}=\sqrt{\frac{3\sqrt{3}-4}{2\sqrt{3}+1}}-\sqrt{\frac{\sqrt{3}+4}{5-2\sqrt{3}}}=\sqrt{\frac{\left(3\sqrt{3}-4\right)\left(2\sqrt{3}-1\right)}{{\left(2\sqrt{3}\right)}^2-1}}-\sqrt{\frac{\left(\sqrt{3}+4\right)\left(5+2\sqrt{3}\right)}{{\left(5\right)}^2-{\left(2\sqrt{3}\right)}^2}}$

$=\sqrt{\frac{22-11\sqrt{3}}{11}}-\sqrt{\frac{26+13\sqrt{3}}{13}}=\sqrt{2-\sqrt{3}}-\sqrt{2+\sqrt{3}}=\sqrt{\frac{4-2\sqrt{3}}{2}}-\sqrt{\frac{4+2\sqrt{3}}{2}}$

$=\frac{1}{\sqrt{2}}\left(\sqrt{{\left(\sqrt{3}-1\right)}^2}-\sqrt{{\left(\sqrt{3}+1\right)}^2}\right)=\frac{1}{\sqrt{2}}\left(\left|\sqrt{3}-1\right|-\sqrt{3}-1\right)=\frac{1}{\sqrt{2}}.\left(-2\right)=-\sqrt{2}$

Vậy $\mathrm{C}=-\sqrt{2}$