1. **State the problem:** Simplify the expression $$|0 + 3| - 4^2 - (-8)| + 2\sqrt{5^2} - 3^2 + (-5)^2|$$. 2. **Rewrite the expression clearly:** $$|0 + 3| - |4^2 - (-8)| + 2\sqrt{5^2} - 3^2 + |(-5)^2|$$ 3. **Calculate inside the absolute values and simplify powers:** - $|0 + 3| = |3| = 3$ - $4^2 = 16$ - $-(-8) = +8$ - So, $|4^2 - (-8)| = |16 + 8| = |24| = 24$ - $5^2 = 25$ - $\sqrt{25} = 5$ - $3^2 = 9$ - $(-5)^2 = 25$, so $|(-5)^2| = |25| = 25$ 4. **Substitute these values back into the expression:** $$3 - 24 + 2 \times 5 - 9 + 25$$ 5. **Perform the multiplications and additions/subtractions step-by-step:** - $2 \times 5 = 10$ - Now the expression is $3 - 24 + 10 - 9 + 25$ 6. **Calculate from left to right:** - $3 - 24 = -21$ - $-21 + 10 = -11$ - $-11 - 9 = -20$ - $-20 + 25 = 5$ **Final answer:** $$5$$