1. Stating the problem: We need to simplify the expression $\sqrt{45} \times \sqrt{20}$.\n\n2. Use the property of square roots: $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$.\n\n3. Apply the property: $$\sqrt{45} \times \sqrt{20} = \sqrt{45 \times 20}$$\n\n4. Multiply inside the square root: $$\sqrt{900}$$\n\n5. Simplify the square root: Since $900 = 30^2$, we have $$\sqrt{900} = 30$$\n\nFinal answer: $30$