Final answer:
To simplify the expression 4 √(3 ÷ 2x), start by simplifying the square root. Then, multiply the numerator and denominator by the conjugate of the denominator and cancel out common factors to get the simplified form 2(√6x) ÷ x.
Step-by-step explanation:
To simplify the expression 4 √(3 ÷ 2x), we can start by simplifying the square root. We know that the square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator. So, the expression becomes 4(√3) ÷ (√2x).
Next, we can simplify further by multiplying the numerator and denominator by the conjugate of the denominator, which is √2x. This leads to 4(√3)(√2x) ÷ (2x).
Finally, we can simplify the expression by canceling out common factors. The final simplified form is 2(√6x) ÷ x.