2x*sqrt(3x^2+4)

To simplify the expression 2x * sqrt(3x^2 + 4), we need to apply the rules of algebra. Let's break down the steps to simplify the given expression:

Step 1: Distribute the 2x term to both terms inside the square root:
2x * sqrt(3x^2 + 4) = 2x * sqrt(3x^2) + 2x * sqrt(4)

Step 2: Simplify each term inside the square root:
sqrt(3x^2) = sqrt(3) * sqrt(x^2) = sqrt(3) * x
sqrt(4) = 2

Substituting the simplified terms back into the expression:

2x * sqrt(3x^2 + 4) = 2x * sqrt(3) * x + 2x * 2
= 2x^2 * sqrt(3) + 4x

Thus, the simplified form of the expression 2x * sqrt(3x^2 + 4) is 2x^2 * sqrt(3) + 4x.