SOLUTION: Rationalize the denominator if necessary. Then simplify each radical expression. Could someone help me I am unable to solve this expression. {{{(6-sqrt(20))/2}}}

Algebra ->  Radicals -> SOLUTION: Rationalize the denominator if necessary. Then simplify each radical expression. Could someone help me I am unable to solve this expression. {{{(6-sqrt(20))/2}}}      Log On


   

Question 98188: Rationalize the denominator if necessary. Then simplify each radical expression. Could someone help me I am unable to solve this expression.
%286-sqrt%2820%29%29%2F2
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!
Rationalize the denominator if necessary. Then simplify each radical expression. Could someone help me I am unable to solve this expression.
%286-sqrt%2820%29%29%2F2

Its denominator 2 is already rational
(contains no roots). So all we can do
is simplify:
Write 20 as 2%2A2%2A5
%286-sqrt%282%2A2%2A5%29%29%2F2
Now write the 2%2A2 as 2%5E2
%286-sqrt%282%5E2%2A5%29%29%2F2
Take individual square roots:
%286-sqrt%282%5E2%29sqrt%285%29%29%2F2
Since sqrt%282%5E2%29 = 2, we have
%286-2sqrt%285%29%29%2F2
Now let's make two fractions by putting
each of the terms over the denominator:
6%2F2-2sqrt%285%29%2F2
Then simplify to:
3-sqrt%285%29
Edwin