SOLUTION: Simplify √(x)+(√(x-3)=3

 +  = 3

Isolate one of the terms with a radical 
(preferably the more complicated one)

        = 3 - 

Square both sides:

    ()² = (3 - )²

        x - 3 = (3 - )(3 - )

        x - 3 = 9 - 3 - 3 + x

        x - 3 = 9 - 6 + x

Simplify and isolate the term with the radical

        6 = 12

Divide both sides by 6

          = 2

Square both sides

        ()² = 2²

         x = 4

We must always check for extraneous (false) solutions
because squaring both sides often introduces them.

 +  = 3
 +  = 3
       2 +  = 3
         2 + 1 = 3
             3 = 3

So x = 4 is the solution.

Edwin