Add or subtract. \( 3 \sqrt{75}-2 \sqrt{50}+\sqrt{12} \) \( 3 \sqrt{75}-2 \sqrt{50}+\sqrt{12}=\square \) (Simplify your answer. Type an exact answer, using radicals as needed.)

To simplify the expression \( 3 \sqrt{75}-2 \sqrt{50}+\sqrt{12} \), we first simplify each square root. 1. Simplifying \( \sqrt{75} \): \[ \sqrt{75} = \sqrt{25 \cdot 3} = 5 \sqrt{3} \] Therefore, \( 3 \sqrt{75} = 3 \cdot 5 \sqrt{3} = 15 \sqrt{3} \). 2. Simplifying \( \sqrt{50} \): \[ \sqrt{50} = \sqrt{25 \cdot 2} = 5 \sqrt{2} \] Thus, \( -2 \sqrt{50} = -2 \cdot 5 \sqrt{2} = -10 \sqrt{2} \). 3. Simplifying \( \sqrt{12} \): \[ \sqrt{12} = \sqrt{4 \cdot 3} = 2 \sqrt{3} \] Now we can rewrite the original expression: \[ 3 \sqrt{75} - 2 \sqrt{50} + \sqrt{12} = 15 \sqrt{3} - 10 \sqrt{2} + 2 \sqrt{3} \] Combining the terms with \( \sqrt{3} \): \[ (15 \sqrt{3} + 2 \sqrt{3}) - 10 \sqrt{2} = 17 \sqrt{3} - 10 \sqrt{2} \] The simplified expression is: \[ 17 \sqrt{3} - 10 \sqrt{2} \] Thus, \[ 3 \sqrt{75}-2 \sqrt{50}+\sqrt{12} = 17 \sqrt{3} - 10 \sqrt{2}. \]