1. **State the problem:** Simplify the expression $\sqrt{450}$. 2. **Recall the formula and rules:** The square root of a product can be expressed as the product of the square roots: $$\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}$$. 3. **Factorize 450:** $$450 = 9 \times 50$$ 4. **Apply the square root to each factor:** $$\sqrt{450} = \sqrt{9 \times 50} = \sqrt{9} \times \sqrt{50}$$ 5. **Simplify the square roots:** $$\sqrt{9} = 3$$ 6. **Simplify $\sqrt{50}$ further by factoring 50:** $$50 = 25 \times 2$$ $$\sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5 \times \sqrt{2}$$ 7. **Combine all simplified parts:** $$\sqrt{450} = 3 \times 5 \times \sqrt{2} = 15 \sqrt{2}$$ **Final answer:** $$\sqrt{450} = 15 \sqrt{2}$$