Question

Simplify : $\frac{\sqrt[3]{38}-\sqrt[3]{3125}}{1-5\sqrt{2}}$

Answer 1

Given:$\frac{\sqrt[3]{38}-\sqrt[3]{3125}}{1-5\sqrt{2}}=\frac{\sqrt[3]{32^3}-\sqrt[3]{35^3}}{1-5\sqrt{2}}$

$=\frac{2-5}{1-5\sqrt{2}}=\frac{3}{5\sqrt{2}-1}$

Multiplying and dividing by $5\sqrt{2}+1$

$=\frac{3}{5\sqrt{2}-1}\times \frac{5\sqrt{2}+1}{5\sqrt{2}+1}$

$=\frac{3(5\sqrt{2}+1)}{51}$