Final answer:
To factor out √6x² when x ≥ 0, we simplify to get 2x multiplied by the square root of 6, yielding the correct answer of 2x√6.
Step-by-step explanation:
To take a factor out of the square root √6x² when x ≥ 0, we need to simplify the expression inside the square root. Since we are given that x is non-negative, we can factor out the square of x from inside the square root.
Firstly, let's look at the expression inside the square root:
- The square of any number, such as x², is always positive or zero.
- The square root of a square, like √x², is simply x for non-negative x.
- The number 6 can be split into two factors: 2² and 1.5 such that 2² * 1.5 = 4 * 1.5 = 6.
Therefore, we can rewrite √6x² as √(2² * 1.5 * x²). Since the square root of a product of numbers is the product of the square roots of those numbers, we get √(2²) * √1.5 * √x² which simplifies to 2x√6.
The correct answer to the question is option b) 2x√6.