e) E = (căn bậc hai 3 + 1) căn bậc hai 14 - 6 căn bậc hai 3/ 5 + căn bậc hai 3

* Hướng dẫn giải

e) Cách 1: $E=\left(\sqrt{3}+1\right)\sqrt{\frac{14-6\sqrt{3}}{5+\sqrt{3}}}=\left(\sqrt{3}+1\right)\sqrt{\frac{\left(14-6\sqrt{3}\right)\left(5-\sqrt{3}\right)}{\left(5+\sqrt{3}\right)\left(5-\sqrt{3}\right)}}$

$=\left(\sqrt{3}+1\right)\sqrt{\frac{88-44\sqrt{3}}{22}}=\left(\sqrt{3}+1\right)\sqrt{4-2\sqrt{3}}=\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)=2$

Cách 2: $E=\left(\sqrt{3}+1\right)\sqrt{\frac{14-6\sqrt{3}}{5+\sqrt{3}}}=\sqrt{\frac{\left(4+2\sqrt{3}\right)\left(14-6\sqrt{3}\right)}{5+\sqrt{3}}}=\sqrt{\frac{20+4\sqrt{3}}{5+\sqrt{3}}}=\sqrt{4}=2$