1. **State the problem:** Simplify the expression $6\sqrt{20} + 7\sqrt{5}$. 2. **Recall the rule:** $\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$ and simplify square roots by factoring out perfect squares. 3. Simplify $\sqrt{20}$: $$\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}$$ 4. Substitute back: $$6\sqrt{20} + 7\sqrt{5} = 6 \times 2\sqrt{5} + 7\sqrt{5} = 12\sqrt{5} + 7\sqrt{5}$$ 5. Combine like terms: $$12\sqrt{5} + 7\sqrt{5} = (12 + 7)\sqrt{5} = 19\sqrt{5}$$ **Final answer:** $19\sqrt{5}$