a) Ta có
$(2\sqrt[3]{5})^3 = 8.5 = 40$
và
$\left( \dfrac{1}{2} \sqrt[3]{311} \right)^3 = \dfrac{1}{8} . 311 < \dfrac{1}{8} . 320 = 40$
Suy ra
$\left( \dfrac{1}{2} \sqrt[3]{311} \right)^3 < (2\sqrt[3]{5})^3$
$\Leftrightarrow \dfrac{1}{2} \sqrt[3]{311} < 2\sqrt[3]{5}$
b) Ta có
$\dfrac{1}{3\sqrt{5} - 7} = \dfrac{3\sqrt{5} + 7}{9.5 - 49} = -\dfrac{3\sqrt{5} + 7}{4}