Rationalizing radical expressions

Question

$\sqrt [ 3 ]{\frac{3}{4} }$ is the expression. What i did was change it to an equivalent fraction $({\sqrt [ 3 ]{\frac{6}{8} }=\frac{\sqrt [ 3 ]{ 6}}{2} } )$. But i think it isn't right. Please help me.

Answer 1

If you did this, you were correct (writing out every possible step):

$$\sqrt[3]{\frac{3}{4}} =\sqrt[3]{\frac{2\times 3}{2\times 4}} =\sqrt[3]{\frac{6}{8}} =\frac{\sqrt[3]{6}}{\sqrt[3]{8}} =\frac{\sqrt[3]{6}}{2} $$