Question

rationalize the denominator. assume that all expressions under radicals represent positive numbers. ^3 sqrt3a / ^3 sqrt2c

Answer 1

\[\sqrt[3]{3a} / \sqrt[3]{2c}\]

Answer 2

\(\bf \cfrac{\sqrt[3]{3a}}{\sqrt[3]{2c}}\cdot \cfrac{\sqrt[3]{(2c)^2}}{\sqrt[3]{(2c)^2}}\implies \cfrac{\sqrt[3]{3a}\cdot \sqrt[3]{(2c)^2}}{\sqrt[3]{2c}\cdot \sqrt[3]{(2c)^2}}\implies \cfrac{\sqrt[3]{3a}\cdot \sqrt[3]{(2c)^2}}{\sqrt[{\color{brown}{ 3}}]{(2c)^{\color{brown}{ 3}}}}\implies ?\)

Answer 3

the idea being, that you'd multiply the denominator, by a value that makes the radicand match the root
thus getting rid of the radical

Answer 4

I have no clue :/ I didn't get this question at all.