1. **State the problem:** Simplify the expression $$\frac{\sqrt{8}}{3} + \frac{\sqrt{32}}{24}$$. 2. **Recall the rules:** - Simplify square roots by factoring out perfect squares. - Find a common denominator to add fractions. 3. **Simplify each square root:** $$\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}$$ $$\sqrt{32} = \sqrt{16 \times 2} = 4\sqrt{2}$$ 4. **Rewrite the expression:** $$\frac{2\sqrt{2}}{3} + \frac{4\sqrt{2}}{24}$$ 5. **Find common denominator:** The denominators are 3 and 24. The least common denominator is 24. 6. **Convert fractions:** $$\frac{2\sqrt{2}}{3} = \frac{2\sqrt{2} \times 8}{3 \times 8} = \frac{16\sqrt{2}}{24}$$ 7. **Add the fractions:** $$\frac{16\sqrt{2}}{24} + \frac{4\sqrt{2}}{24} = \frac{(16\sqrt{2} + 4\sqrt{2})}{24} = \frac{20\sqrt{2}}{24}$$ 8. **Simplify the fraction:** $$\frac{20}{24} = \frac{5}{6}$$ 9. **Final simplified expression:** $$\frac{5\sqrt{2}}{6}$$