Final answer:
The correct way to take a factor out of the square root of √(6x^2) is by separating the terms under the root and simplifying to get √6 * √x, which corresponds to option d).
Step-by-step explanation:
To take a factor out of the square root of √(6x^2) with the constraint that x ≥ 0, we use the property that the square root of a product is equal to the product of the square roots of the factors. Thus, we separate 6 and x^2 under the square root:
√(6x^2) = √(6) * √(x^2)
Since x is non-negative, we can simplify √(x^2) to x, and our expression becomes:
√(6) * x
Therefore, the correct factor taken out of the square root is √(6) * √x, which matches option d) √6 * √x.