How do you rationalize the denominator and simplify $root3(2/3)$ ?

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Answer 1 · 2016-03-30T23:36:43

$root(3)(2/3) = root(3)(18)/3$

If $a, b > 0$ then $root(n)(a/b) = root(n)(a)/root(n)(b)$

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

$root(3)(2/3) = root(3)((2*9)/(3*9)) = root(3)(18/3^3) = root(3)(18)/3$

How do you rationalize the denominator and simplify root3(2/3)root3(2/3)?