Expert: Ahmed Salami - 10/5/2004

Question
Hi Ahmed.

I have a very basic question about simplifying square roots.
I can not remember how to remove the perfect square factors from
under the square root sign such as the one below:
(pretend that the number is under the square root sign)16200
 
I'd appreciate if you could take me through the steps... Thanks.

Clara  

Answer
Hi Clara,
Basically, you just have to start by trying to identify the perfect squares you recognise as factors. You can always start with 4,followed by 9,16,25 but this could be tedious at times if you have a very large number. So we can at times use a larger number if we can. As an example, in this case i've spotted 100 as a factor.
16200 = 162 x 100
4 is not a factor of 162 but 9 is
162 = 9 x 9 x 2 = 81 x 2
So, in the end
16200 = 2 x 81 x 100
Therefore,
sqrt(16200)= sqrt(2).sqrt(81). sqrt(100)
          = 9.10.sqrt(2)
          = 90.[sqrt(2)]
which shows that 16200 itself is not a perfect square.
I hope i have helped you.
Regards.