1. **State the problem:** Simplify the expression $y\sqrt{20} + \sqrt{80y^2}$ assuming all variables are positive. 2. **Recall the rules:** - The square root of a product can be written as the product of square roots: $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$. - Since variables are positive, $\sqrt{y^2} = y$. 3. **Simplify each term:** - $y\sqrt{20} = y\sqrt{4 \times 5} = y \times \sqrt{4} \times \sqrt{5} = y \times 2 \times \sqrt{5} = 2y\sqrt{5}$. - $\sqrt{80y^2} = \sqrt{80} \times \sqrt{y^2} = \sqrt{16 \times 5} \times y = \sqrt{16} \times \sqrt{5} \times y = 4y\sqrt{5}$. 4. **Combine like terms:** - $2y\sqrt{5} + 4y\sqrt{5} = (2y + 4y)\sqrt{5} = 6y\sqrt{5}$. **Final answer:** $$6y\sqrt{5}$$