Solve a Square root Problem

1.  How find the Square root of 256.

                     Prime factorisation of 256 is

256 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

By pairing the prime factors we get,

256 = 2 x 2 x 2 x 2 x 2 x 2  2 x 2 

or        256 = (2 x 2 x 2 x 2)²

 Therefore,  √256 = 2 x 2 x 2 x 2  = 16  solution.

2. How find the Square root of 6400.

               Prime factorisation of 6400 is

          6400 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5

By pairing the prime factors we get,

6400 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 5 x 5

or     256 = (2 x 2 x 2 x 2 x 5)²

Therefore,  
              √6400 = 2 x 2 x 2 x 2 x 5 = 80  solution.