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

Question

I dont know how to do 

root 1-2root2/3 all divided by 2

Answer 1

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