Sorry, the question I typed was wrong. I wanted to ask: Why can't the square root of 120 be the square root of 12 and the square root of 10? Because 12 x 10= 120.

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sqrt12*sqrt10=sqrt120. However, if you're adding, you can't do anything with the roots.

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.