SOLUTION: Please help me with the following two problems: Thank you! Perform the indicated division. Rationalize the denominator if necessary. Then simplify each radical expression.

Algebra ->  Radicals -> SOLUTION: Please help me with the following two problems: Thank you! Perform the indicated division. Rationalize the denominator if necessary. Then simplify each radical expression.       Log On


   

Question 105182: Please help me with the following two problems: Thank you!
Perform the indicated division. Rationalize the denominator if necessary. Then simplify each radical expression.
-9-sqrt108
__________
3


6-sqrt20
__________
2
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
:
We can write it:
%28%289-sqrt%28108%29%29%29%2F3
:
the perfects squares that are factors of 108
%28%289-sqrt%284%2A9%2A3%29%29%29%2F3
:
Extract the squares
%28%289-2%2A3%2Asqrt%283%29%29%29%2F3
which is
%28%289-6%2Asqrt%283%29%29%29%2F3
Same as:
9%2F3 - %28%286%2Asqrt%283%29%29%29%2F3
Cancel the 3's and you have:
3 - 2%2Asqrt%283%29
:
:
Do much the same thing here:
%28%286-sqrt%2820%29%29%29%2F2
:
%28%286-sqrt%284%2A5%29%29%29%2F2
:
%28%286-2%2Asqrt%285%29%29%29%2F2
:
The 2 divides into 6 and 2 leaving you with:
3 - sqrt%285%29