1. The problem is to add two irrational numbers and simplify the result. 2. First example: $\sqrt{3} + (-\sqrt{3}) = \sqrt{3} - \sqrt{3} = 0$. This shows that adding a number and its negative results in zero. 3. Second example: $5\sqrt{13} + 2\sqrt{13} = (5 + 2)\sqrt{13} = 7\sqrt{13}$. Approximating $\sqrt{13} \approx 3.6055$, we get $7 \times 3.6055 = 25.2385$. 4. Third example: $(4\sqrt{5} - \sqrt{5}) + \sqrt{5} = (4 - 1 + 1)\sqrt{5} = 4\sqrt{5}$. Approximating $\sqrt{5} \approx 2.2360$, we get $4 \times 2.2360 = 8.944$. 5. Summary: When adding irrational numbers with the same radical part, add their coefficients and multiply by the radical. Final answers: - $\sqrt{3} + (-\sqrt{3}) = 0$ - $5\sqrt{13} + 2\sqrt{13} = 7\sqrt{13} \approx 25.2385$ - $(4\sqrt{5} - \sqrt{5}) + \sqrt{5} = 4\sqrt{5} \approx 8.944$