1. **State the problem:** Calculate the value of $$\sqrt{270(270-120)(270-170)(270-250)}$$. 2. **Simplify the terms inside the square root:** $$270 - 120 = 150$$ $$270 - 170 = 100$$ $$270 - 250 = 20$$ 3. **Rewrite the expression:** $$\sqrt{270 \times 150 \times 100 \times 20}$$ 4. **Multiply the numbers inside the square root:** First multiply pairs: $$270 \times 150 = 40500$$ $$100 \times 20 = 2000$$ Then multiply the results: $$40500 \times 2000 = 81,000,000$$ 5. **Calculate the square root:** $$\sqrt{81,000,000} = 9000$$ **Final answer:** $$9000$$