SOLUTION: How would you write the following expression with a rational denominator and in simplest form?: {{{5/(sqrt(2)+ sqrt(3))}}} I have a test tomorrow and myself and most of the

Algebra ->  Rational-functions -> SOLUTION: How would you write the following expression with a rational denominator and in simplest form?: {{{5/(sqrt(2)+ sqrt(3))}}} I have a test tomorrow and myself and most of the      Log On


   

Question 176975: How would you write the following expression with a rational denominator and in simplest form?:
5%2F%28sqrt%282%29%2B+sqrt%283%29%29

I have a test tomorrow and myself and most of the people in my algebra class are still extremely confused. Please, please, please, help me with this and explain in full detail if possible! You're help would be very much appreciated!
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
When they are asking you to write it in "rational" form, they do not want to see any radicals (square root symbols) in the denominator.
.
5%2F%28sqrt%282%29%2B+sqrt%283%29%29
.
Multiply by the above by: %28sqrt%282%29-+sqrt%283%29%29%2F%28sqrt%282%29-+sqrt%283%29%29
.

.
5%28sqrt%282%29-+sqrt%283%29%29%2F%282+-+3%29%29
.
5%28sqrt%282%29-+sqrt%283%29%29%2F%28-1%29
.
5%28sqrt%283%29-+sqrt%282%29%29
.
or,
5sqrt%283%29-+5sqrt%282%29