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

I dont know how to do
root 1-2root2/3 all divided by 2

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
----------
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