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

1 Answer
Mar 30, 2016

Answer:

#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#