1. **State the problem:** Evaluate the expression $$\sqrt{(-3)^2} + \sqrt{| -4 |}$$. 2. **Recall the rules:** - The square root of a squared number is the absolute value of the original number, i.e., $$\sqrt{x^2} = |x|$$. - The absolute value function $$|x|$$ returns the non-negative value of $$x$$. 3. **Evaluate each part:** - Calculate $$(-3)^2 = 9$$. - Then $$\sqrt{(-3)^2} = \sqrt{9} = 3$$ (since $$\sqrt{x^2} = |x|$$). - Calculate $$| -4 | = 4$$. - Then $$\sqrt{| -4 |} = \sqrt{4} = 2$$. 4. **Add the results:** $$3 + 2 = 5$$. **Final answer:** $$5$$.