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how do i simplify -Radical 1-2 root2/3 all divided by 2

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1 Answer

I believe your question looks like this? :
 
  √(1)-2√(2/3)
-----------------
         2
 
The root of 1 is 1:
 
 1-2√(2/3)
-----------
      2
 
This is the same as:
 
 1       2√(2/3)
---  -  ---------
 2            2
 
Let us deal with the root in the numerator first:
 
  Because it is a root of the fraction, both the numerator and denominator can receive their own separate roots:
 
2√(2/3)  =  2√2 ⁄ √3
 
so:
 
 1       2√2 / √3
---  -  ----------
 2            2
 
now we have division of fractions, so the problem becomes:
 
 1       2√2      2
---  -  ------  * ---
 2       √3        1
 
then:
 
 1       4√2
---  -  ------
 2        √3
 
we don't like to see roots in our denominator, so we multiply the numerator and denominator by √3, giving:
 
 1       4√2√3
---  -  ---------
 2           3
 
we can multiply our roots:
 
 1       4√6
---  -  ------
 2         3
 
our LCD is 6, so:
 
 3 - 8√6
----------
     6