Final answer:
The expression 3 √12x² simplifies to 6x √3, by factoring out the perfect squares under the radical and taking them outside the radical sign.
Step-by-step explanation:
The task here is to simplify the mathematical expression 3 √12x², assuming y ≠ 0. First, we break down the number under the radical. The number 12 can be expressed as 4 × 3, where 4 is a perfect square. Therefore, 3 √12x² can be rewritten as 3 √(4×3)x². We can then take the square root of 4 and x² out of the radical since both are perfect squares.
Next, we simplify the expression:
- 3 √(4×3)x² = 3 √4 √3 √x²
- 3 × 2 × x √3 = 6x √3
Therefore, the simplified form of the expression is 6x √3, which matches option A) 6√3x.