Simplify the expression. \[ 15 \sqrt{5}+6 \sqrt{20} \]

To simplify the expression \( 15 \sqrt{5}+6 \sqrt{20} \), we start by simplifying \( \sqrt{20} \). We know that: \[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \cdot \sqrt{5} = 2 \sqrt{5} \] Now we can substitute this back into the expression: \[ 6 \sqrt{20} = 6 \cdot 2 \sqrt{5} = 12 \sqrt{5} \] Now the expression becomes: \[ 15 \sqrt{5} + 12 \sqrt{5} \] Next, we can combine the like terms: \[ (15 + 12) \sqrt{5} = 27 \sqrt{5} \] Thus, the simplified expression is: \[ \boxed{27 \sqrt{5}} \]