Question

Since  768  is an even number and  4  is a perfect square, I'm going to divide  768  by  4:

     768  =  4 x 192

Since  193  is an even number and  4  is a perfect square, I'm going to divide  192  by  4:

     768  =  4 x 4 x 48

Since  48  is an even number and  4  is a perfect square, I'm going to divide  48  by  4:

     768  =  4 x 4 x 4 x 12

Since  12  is an even number and  4  is a perfect square, I'm going to divide  12  by  4:

     768  =  4 x 4 x 4 x 4 x 3

So, the  sqrt(768)  =  2 x 2 x 2 x 2 x sqrt(3)  =  16 x sqrt(3).

sqrt(768) =sqrt(2^8) x sqrt(3) =2^4 x sqrt(3)=16sqrt(3)