1. **State the problem:** Multiply $6\sqrt{5}$ by $\sqrt{5}$. 2. **Recall the multiplication rule for radicals:** $\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}$. 3. **Apply the rule:** $6\sqrt{5} \times \sqrt{5} = 6 \times \sqrt{5 \times 5}$. 4. **Simplify inside the radical:** $\sqrt{5 \times 5} = \sqrt{25}$. 5. **Evaluate the square root:** $\sqrt{25} = 5$. 6. **Multiply the constants:** $6 \times 5 = 30$. 7. **Final answer:** $6\sqrt{5} \times \sqrt{5} = 30$.