Solving limits by change of variable

I learned today that one of the methods for solving a limit is by change of variable. However, I'm confused as to how it works. I have the following question as an example:

Evaluate the limit by change of variable.

lim x->8

3√x - 2

______

x-8

I started by saying let 3√x = y. So the numerator becomes y-2. However, I'm uncertain how to change the denominator when solving by change of variable , and how to determine what the new lim y-> is (are there general rules for these?). Thank you so much for any help, as I have a test on this on Friday.