Algebra
posted by Amelie .
I need to rationalize the denominator of 2/3 square root of five, (three being the index). My book suggests you should multiply this by 3 square root of 5^2 over 3 square root of 5^2. I thought the numbers that you rationalize the original with should be the denominator unaltered. Why do you add a ^2 to the 5? Thanks for your help!!!

are you sure this is not
2
____
5^(1/3)
?

If that is the case, you need to get 5^1 = 5 on the bottom
The way to do that is to multiply top and bottom by
5^(2/3)
2 * 5^(2/3)
______________
5^(1/3) * 5^(2/3)
which is
2 * 5^2/3
__________
5