1. **State the problem:** Calculate the value of $\frac{24 + \sqrt{3}}{11}$.\n\n2. **Formula and explanation:** This is a simple arithmetic expression involving addition and division. The square root symbol $\sqrt{3}$ represents the positive number which when squared gives 3.\n\n3. **Intermediate work:**\n- First, calculate $\sqrt{3}$ approximately, which is about 1.732.\n- Then add 24 to this value: $24 + 1.732 = 25.732$.\n- Finally, divide this sum by 11: $\frac{25.732}{11} \approx 2.339$.\n\n4. **Final answer:**\n$$\frac{24 + \sqrt{3}}{11} \approx 2.339$$\nThis is the simplified numerical value of the given expression.