SOLUTION: I have to simplify {{{4/(3sqrt(5)+sqrt(3))}}} I have no idea how to do this please help!

Algebra ->  Square-cubic-other-roots -> SOLUTION: I have to simplify {{{4/(3sqrt(5)+sqrt(3))}}} I have no idea how to do this please help!       Log On


   



Question 704154: I have to simplify 4%2F%283sqrt%285%29%2Bsqrt%283%29%29

I have no idea how to do this please help!

Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!
4%2F%283sqrt%285%29%2Bsqrt%283%29%29

The procedure is: 

1. Put parentheses around the denominator:
2. Create the conjugate of the denominator and put it in parentheses
3. Put that conjugate over itself (which has value 1)
4. Multiply by that.  (multiplying it won't affect the value since it equals 1)

1. Put denominator in parentheses: 4%2F%28%283sqrt%285%29%2Bsqrt%283%29%29%29

2. To create the conjugate of 3sqrt%285%29%2Bsqrt%283%29, just change the
   sign of the second term, making the conjugate 3sqrt%285%29-sqrt%283%29.
   Put it in parentheses %283sqrt%285%29-sqrt%283%29%29.
3. Put that conjugate over itself, like this %28%283sqrt%285%29-sqrt%283%29%29%29%2F%28%283sqrt%285%29-sqrt%283%29%29%29
4. Multiply by that:

4%2F%28%283sqrt%285%29%2Bsqrt%283%29%29%29%22%22%2A%22%22%28%283sqrt%285%29-sqrt%283%29%29%29%2F%28%283sqrt%285%29-sqrt%283%29%29%29




FOIL out the bottom:



The two middle terms cancel out on the bottom:



%284%282sqrt%285%29-sqrt%283%29%29%29%0D%0A%0D%0A%0D%0A%2F%289sqrt%2825%29-sqrt%289%29%29

On the bottom, sqrt%2825%29 is just 5 and sqrt%289%29 is just 3

%284%283sqrt%285%29-sqrt%283%29%29%29%0D%0A%0D%0A%0D%0A%2F%289%2A5-3%29

%284%283sqrt%285%29-sqrt%283%29%29%29%0D%0A%0D%0A%0D%0A%2F%2845-3%29

%284%283sqrt%285%29-sqrt%283%29%29%29%0D%0A%0D%0A%0D%0A%2F42

Divide top and bottom by 2

%282%283sqrt%285%29-sqrt%283%29%29%29%0D%0A%0D%0A%0D%0A%2F21

Edwin