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Answer :
Final answer:
The correct simplified form of the expression √(3x³(2x² - 4x - 3)) is x²√(6x) - 2x²√(12) - 9x². The correct option is not listed here.
Explanation:
The student is asking to simplify the expression √(3x³(2x² - 4x - 3)). To simplify this radical expression, it is important to recognize that the square root function √() and the exponentiation involved in raising something to the power of 3 (³) are inverse operations for the variable x, since √(x³) = x¹µ = x(1.5) = x³/2. This relationship allows us to simplify the expression inside the square root before taking the actual square root. Let's see how this is done:
- First, distribute the exponent inside the parentheses: √(3x³ × 2x²) - √(3x³ × 4x) - √(3x³ × 3).
- This results in √(6xµ) - √(12x´) - √(9x³).
- Then, apply the square root to each term: x²√(6x) - 2x²√(12) - 3x¹µ√(9).
- Since the square roots of 6, 12, and 9 are not perfect squares, they remain under the square root. However, √(9) simplifies to 3.
- The final simplified expression is x²√(6x) - 2x²√(12) - 9x².
- Seeing as none of the answer choices match this expression, it indicates that there might be a mistake in the problem statement or in the provided options.
Therefore, without matching options, the correct simplified form does not appear among the choices given. This would be a situation where the student should review the question and provided answers or seek clarification. Furthermore, the provided information in the original question does not directly relate to this simplification problem and is likely not applicable.
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