Question 43691
<pre><font size = 4><b> 
    7
---------
 &#8730;3 – &#8730;2


To rationalize a denominator with has two terms, you must

1. Form the conjugate surd
   A.  Write the denominator &#8730;3 - &#8730;2
   B. Change the sign of the second term only &#8730;3 + &#8730;2
   

2. Form the fraction by putting the conjugate surd over
   itself. 

    &#8730;3 + &#8730;2
   ---------   (Notice that this equals the number 1]
    &#8730;3 + &#8730;2

3. Multiply the original fraction by this fraction.  The
   value won't change because this amounts to multiplying
   by 1.

      7        &#8730;3 + &#8730;2
  --------- × ---------
   &#8730;3 – &#8730;2     &#8730;3 + &#8730;2

4. Indicate the multiplication of numerators ans denominators

       7(&#8730;3 + &#8730;2)
  -------------------
   (&#8730;3 – &#8730;2)(&#8730;3 + &#8730;2)    
  
5.  Multiply the top and the bottom  

           7&#8730;3 + 7&#8730;2
   ------------------------
      3 + &#8730;3&#8730;2 - &#8730;2&#8730;3 - 2

6. The middle two terms in the bottom cancel out

    7&#8730;3 + 7&#8730;2
   -----------
      3 - 2

    7&#8730;3 + 7&#8730;2
   -----------
        1

    7&#8730;3 + 7&#8730;2
  
Edwin
AnlytcPhil@aol.com</pre>