1. **State the problem:** We need to find the value of $$\sqrt{x^2 + y^2}$$ when $$x = -3$$ and $$y = -4$$. 2. **Formula used:** The expression $$\sqrt{x^2 + y^2}$$ represents the distance from the origin to the point $$(x, y)$$ in the coordinate plane, calculated using the Pythagorean theorem. 3. **Substitute the values:** Replace $$x$$ and $$y$$ with the given values: $$\sqrt{(-3)^2 + (-4)^2}$$ 4. **Calculate the squares:** $$\sqrt{9 + 16}$$ 5. **Add the values inside the square root:** $$\sqrt{25}$$ 6. **Find the square root:** $$5$$ **Final answer:** The value of $$\sqrt{x^2 + y^2}$$ when $$x = -3$$ and $$y = -4$$ is **5**.