SOLUTION: This question is about how to divide radical expressions. I have the basic idea to divide roots just not radical expressions. 2/SQRT5+2 I know the next step is to rationaize

Algebra ->  Square-cubic-other-roots -> SOLUTION: This question is about how to divide radical expressions. I have the basic idea to divide roots just not radical expressions. 2/SQRT5+2 I know the next step is to rationaize      Log On


   

Question 274869: This question is about how to divide radical expressions. I have the basic idea to divide roots just not radical expressions.
2/SQRT5+2 I know the next step is to rationaize the denominator so problem reads 2/SQRT5+2 * SQRT5+2/SQRT5+2= 2SQRT5+2/(SQRT5+2)^2 this is where i am confused what to next or maby I multiplied wrong. Any help be much appreciated. Thank you.
Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
2%2F%28sqrt%285%29%2B2%29
To rationalize a two-term denominator like this you multiply the numerator and denominator by the conjugate of the denominator. The conjugate of sqrt%285%29%2B2 is sqrt%285%29-2. (Note the minus sign!)

You should be familiar with the pattern: %28a%2Bb%29%28a-b%29+=+a%5E2+-+b%5E2. a+b and a-b are conjugates of each other. And as you can see, when you multiply conjugates you get two terms which are both perfect squares. This is why we use conjugates when rationalizing denominators. The only terms in the priduct are perfect squares.
%282%2F%28sqrt%285%29%2B2%29%29%28%28sqrt%285%29-2%29%2F%28sqrt%285%29-2%29%29
Multiplying we get:
%282%28sqrt%285%29-2%29%29%2F%28%28sqrt%285%29%29%5E2+-+2%5E2%29
which simplifies to:
%282sqrt%285%29-4%29%2F%285-4%29
or
%282sqrt%285%29-4%29%2F1
or
2sqrt%285%29-4
Not only do we no longer have a radical in a denominator, we have no denominator at all!