Example 1: Multiplying Identical Radicals

Problem: Multiply $6\sqrt{5}$ by $2\sqrt{5}$

1. Group the parts: Multiply the whole numbers together and the radicals together: $(6 \times 2) \times (\sqrt{5} \times \sqrt{5})$

2. Simplify: $12 \times 5$

3. Result: $60$

Example 2: Multiplying Different Radicals

Problem: Multiply $2\sqrt{8}$ by $5\sqrt{2}$

1. Group the parts: Multiply whole numbers $(2 \times 5)$ and combine the radicals $\sqrt{8 \times 2}$

2. Multiply: $10\sqrt{16}$

3. Simplify the square root: Since $\sqrt{16} = 4$, the expression becomes $10(4)$

4. Result: $40$