Question: 3\sqrt{8} + 7\sqrt{80} - \sqrt{18} - 3\sqrt{125} =
1. **State the problem:** Simplify the expression $$3\sqrt{8} + 7\sqrt{80} - \sqrt{18} - 3\sqrt{125}$$.
2. **Recall the rule:** To simplify expressions with square roots, factor the radicand into perfect squares and simplify using $$\sqrt{a^2 \times b} = a\sqrt{b}$$.
3. **Simplify each term:**
- $$3\sqrt{8} = 3\sqrt{4 \times 2} = 3 \times 2 \sqrt{2} = 6\sqrt{2}$$
- $$7\sqrt{80} = 7\sqrt{16 \times 5} = 7 \times 4 \sqrt{5} = 28\sqrt{5}$$
- $$\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}$$
- $$3\sqrt{125} = 3\sqrt{25 \times 5} = 3 \times 5 \sqrt{5} = 15\sqrt{5}$$
4. **Rewrite the expression with simplified terms:**
$$6\sqrt{2} + 28\sqrt{5} - 3\sqrt{2} - 15\sqrt{5}$$
5. **Group like terms:**
$$ (6\sqrt{2} - 3\sqrt{2}) + (28\sqrt{5} - 15\sqrt{5}) $$
6. **Combine coefficients:**
$$ 3\sqrt{2} + 13\sqrt{5} $$
7. **Final answer:**
$$\boxed{3\sqrt{2} + 13\sqrt{5}}$$