7. Simplify a)

Since this is a cube root, group the factors in groups of 3.



Three factors inside the cube root is the same as one factor outside the cube root.



There are now no variables which have 3 or more factors inside the radical, but this is still not simplified because there is a denominator under the radical. We must rationalize the denominator. In order to bring out a factor of z in the bottom, there would need to be 3 factors of z under the radical. We have 2 factors of z in the bottom under the radical, so we need one more. We can multiply the bottom by another factor of z so long as we multiply the top by the same thing.



Three z's in the bottom under the radical is the same as one z outside the radical in the bottom.



return to problem 7