1. **State the problem:** Simplify the expression $\sqrt{50} + \sqrt{78}$. 2. **Recall the formula and rules:** The square root of a product can be expressed as the product of square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. We simplify square roots by factoring out perfect squares. 3. **Simplify each square root:** - $\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2}$ - $\sqrt{78} = \sqrt{39 \times 2}$. Since 39 is not a perfect square and has no perfect square factors other than 1, it remains $\sqrt{78} = \sqrt{39 \times 2} = \sqrt{39} \times \sqrt{2}$ but $\sqrt{39}$ cannot be simplified further, so we keep it as $\sqrt{78}$ or factor as $\sqrt{2} \times \sqrt{39}$. 4. **Rewrite the expression:** $$\sqrt{50} + \sqrt{78} = 5\sqrt{2} + \sqrt{78}$$ 5. **Check for like terms:** We can write $\sqrt{78}$ as $\sqrt{2 \times 39} = \sqrt{2} \times \sqrt{39}$, but since $\sqrt{39}$ is irrational and different from 5, the terms are not like terms and cannot be combined further. 6. **Final simplified form:** $$5\sqrt{2} + \sqrt{78}$$ This is the simplest exact form of the expression. **Answer:** $5\sqrt{2} + \sqrt{78}$