1. **State the problem:** Simplify the expression $$\sqrt{12} - \sqrt{75} + \sqrt{147}$$. 2. **Recall the rule:** The square root of a product can be written as the product of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. We use this to simplify each radical by factoring out perfect squares. 3. **Simplify each term:** - $$\sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3}$$ - $$\sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3}$$ - $$\sqrt{147} = \sqrt{49 \times 3} = \sqrt{49} \times \sqrt{3} = 7\sqrt{3}$$ 4. **Rewrite the expression:** $$2\sqrt{3} - 5\sqrt{3} + 7\sqrt{3}$$ 5. **Combine like terms:** Since all terms have $$\sqrt{3}$$, combine coefficients: $$ (2 - 5 + 7)\sqrt{3} = 4\sqrt{3} $$ **Final answer:** $$4\sqrt{3}$$