To find the average rate of change of a function over an interval, we use the formula: Average Rate of Change = (f(b) - f(a)) / (b - a), where [a, b] is the interval. In this case, we have the function f(x) = 2√(x+4) - 3 and the interval [2, 3]. First, we calculate the function values at the endpoints: f(2) = 2√(2+4) - 3 = 2√6 - 3 and f(3) = 2√(3+4) - 3 = 2√7 - 3. The difference in function values is f(3) - f(2) = (2√7 - 3) - (2√6 - 3) = 2√7 - 2√6. The difference in input values is 3 - 2 = 1. Therefore, the average rate of change is (2√7 - 2√6) / 1 = 2√7 - 2√6. To find a numerical approximation, you can calculate the values of √7 and √6 and substitute them into the expression.