How do you rationalize the denominator and simplify $\sqrt[3]{\frac{2}{3}}$ $root3(2/3)$ ?

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How do you rationalize the denominator and simplify $\sqrt[3]{\frac{2}{3}}$ $root3(2/3)$ ?

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Answer 1 · 2016-03-30T23:36:43

$\sqrt[3]{\frac{2}{3}} = \frac{\sqrt[3]{18}}{3}$ $root(3)(2/3) = root(3)(18)/3$

Explanation:

If $a, b > 0$ $a, b > 0$ then $\sqrt[n]{\frac{a}{b}} = \frac{\sqrt[n]{a}}{\sqrt[n]{b}}$ $root(n)(a/b) = root(n)(a)/root(n)(b)$

In our example, rationalize before splitting the cube root by multiplying both numerator and denominator of the radicand by $9$ $9$ :

$\sqrt[3]{\frac{2}{3}} = \sqrt[3]{\frac{2 \cdot 9}{3 \cdot 9}} = \sqrt[3]{\frac{18}{3^{3}}} = \frac{\sqrt[3]{18}}{3}$ $root(3)(2/3) = root(3)((2*9)/(3*9)) = root(3)(18/3^3) = root(3)(18)/3$

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How do you rationalize the denominator and simplify $\sqrt[3]{\frac{2}{3}}$ $root3(2/3)$ ?

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