simplify and rationalise 1/ sqrt(12)

1. Start by simplifying the denominator  

          - We can write sqrt(12) as sqrt (4*3). 

          - This can be written as sqrt(4) * sqrt(3) 

          - We know the square root of 4 is 2. sqrt(3) is not a integer so we leave that as sqrt(3). 

         - So Sqrt(12) = 2*sqrt(3)

2. We now have 1 / 2*sqrt(3). We want to make the denominator rational and to do this we need to get rid of the surd on the bottom. 

          - We will multiply 1 / 2*sqrt(3) by sqrt(3) / sqrt(3) (we can do this becasue this is the same as multiplying by 1) 

          - We now have 1sqrt(3) / 2sqrt(3)*sqrt(3) 

          - 1*sqrt(3) = sqrt(3). 

          - sqrt(3)sqrt(3) = 3. 32 = 6 

3. Our answer is sqrt(3) / 6.