Well it can and it can't. That's an acceptable way to start simplifying the sqrt of 120 algebraically, but it's not complete.
sqrt 120 = sqrt 12*10... fine, but you've got to break it into prime factorization to simplify.
So, sqrt 120 = sqrt 2*2*2*3*5. Then you take out any pairs. Here we have a pair of 2's.
Sqrt 120 = sqrt 2*2*2*3*5 = 2 sqrt 2*3*5 (then multiply everything together so it's in the smallest possible form to get:
2 sqrt 30
Note: The reason only 2 comes out, instread of 4, is that you have to actually take the sqrt of a number to pull it out of the radical. So a pair of 2's in the radical equals one 2 outside the radical.