17) \( -3 \sqrt{15}(5+\sqrt{3}) \)

To simplify \( -3 \sqrt{15}(5+\sqrt{3}) \), we use the distributive property. This means we multiply \( -3 \sqrt{15} \) by both \( 5 \) and \( \sqrt{3} \): 1. First, calculate \( -3\sqrt{15} \times 5 = -15\sqrt{15} \). 2. Next, calculate \( -3\sqrt{15} \times \sqrt{3} = -3\sqrt{15 \times 3} = -3\sqrt{45} \). 3. Since \( \sqrt{45} = 3\sqrt{5} \), we further simplify \( -3\sqrt{45} \) to \( -9\sqrt{5} \). Putting it all together, we have: \[ -15\sqrt{15} - 9\sqrt{5} \] That's your simplified expression!