7sqrt(3) is broken down. sqrt(12) is not broken down. Let's find all the factors of 12 and see if we stumble on a perfect square: 1 * 12 2 * 6 3 * 4 4 is a perfect square, since sqrt(4) = 2. So sqrt(12) = sqrt(3 * 4) We pull the sqrt(4) = 2 outside the radical and rewrite our problem as: 7sqrt(3) - 2sqrt(3) These are like terms, so we have: (7 - 2)sqrt(3) 5sqrt(3)
