Simplify the expression \( 15 \sqrt{5}+6 \sqrt{20} \)

To simplify the expression \( 15 \sqrt{5} + 6 \sqrt{20} \), follow these steps: 1. **Simplify \(\sqrt{20}\):** Break down 20 into its prime factors to simplify the square root. \[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5} \] 2. **Substitute back into the original expression:** Replace \(\sqrt{20}\) with \(2\sqrt{5}\). \[ 15 \sqrt{5} + 6 \sqrt{20} = 15 \sqrt{5} + 6 \times 2\sqrt{5} \] \[ = 15 \sqrt{5} + 12 \sqrt{5} \] 3. **Combine like terms:** Since both terms have \(\sqrt{5}\), you can add their coefficients. \[ 15 \sqrt{5} + 12 \sqrt{5} = (15 + 12) \sqrt{5} = 27 \sqrt{5} \] **Final Simplified Expression:** \[ 27 \sqrt{5} \]