Question

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

Answer 1

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

Explanation:

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`