1. **State the problem:** Simplify the expression $20\sqrt{20} \div 4\sqrt{4}$. 2. **Recall the properties:** The square root of a product can be separated as $\sqrt{a} \times \sqrt{b} = \sqrt{ab}$, and division of terms can be written as a fraction. 3. **Rewrite the expression:** $$\frac{20\sqrt{20}}{4\sqrt{4}}$$ 4. **Simplify the constants:** $$\frac{20}{4} = 5$$ 5. **Simplify the square roots:** $$\sqrt{4} = 2$$ 6. **Rewrite the expression with simplified parts:** $$\frac{5\sqrt{20}}{2}$$ 7. **Simplify $\sqrt{20}$:** $$\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}$$ 8. **Substitute back:** $$\frac{5 \times 2\sqrt{5}}{2}$$ 9. **Multiply numerator:** $$\frac{10\sqrt{5}}{2}$$ 10. **Simplify the fraction:** $$\frac{\cancel{10}\sqrt{5}}{\cancel{2}} = 5\sqrt{5}$$ **Final answer:** $5\sqrt{5}$