1. **State the problem:** Calculate the value of the expression $$24 \cdot (27 - 6) \div 3 - \sqrt{25 \cdot 3}$$. 2. **Apply order of operations (PEMDAS/BODMAS):** - Parentheses first - Then multiplication and division from left to right - Then subtraction - Square root is evaluated as part of parentheses or exponents 3. **Calculate inside the parentheses:** $$27 - 6 = 21$$ 4. **Substitute back:** $$24 \cdot 21 \div 3 - \sqrt{25 \cdot 3}$$ 5. **Multiply and divide from left to right:** $$24 \cdot 21 = 504$$ 6. **Divide:** $$504 \div 3 = 168$$ 7. **Calculate the square root term:** $$25 \cdot 3 = 75$$ 8. **Square root:** $$\sqrt{75} = \sqrt{25 \cdot 3} = 5\sqrt{3}$$ 9. **Substitute back:** $$168 - 5\sqrt{3}$$ 10. **Final answer:** $$168 - 5\sqrt{3}$$ This is the simplified exact form of the expression.