How do you simplify $\frac{\sqrt[3]{2}}{\sqrt[3]{6}}$ $root3 2/root3 6$ ?

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Answer 1 · 2016-03-17T12:54:47

$\frac{\sqrt[3]{2}}{\sqrt[3]{6}} = \frac{\sqrt[3]{3^{2}}}{3} = \frac{\sqrt[3]{9}}{3}$ $root3(2)/root3(6)=root3(3^2)/3=root3(9)/3$

$root3(2)/root3(6)=root3(cancel(2)^color(magenta)1/cancel(6)^color(magenta)3)=root3(1/3)=1/root3(3)$

Now the radical is in a form that could be rationalized

$1/root3(3)=1/root3(3)*root3(3^2)/root3(3^2)=root3(3^2)/3$

How do you simplify root3 2/root3 63√23√6root3 2/root3 6?