2) \( -6 \sqrt[3]{5000}+\sqrt{20}+8 \sqrt[3]{40}-3 \sqrt{32} \)

To simplify the expression \( -6 \sqrt[3]{5000}+\sqrt{20}+8 \sqrt[3]{40}-3 \sqrt{32} \), let's break it down step by step. 1. **Cube Roots**: - \( \sqrt[3]{5000} = \sqrt[3]{5^4 \times 2^3} = 10 \sqrt[3]{5} \) (since \( 5000 = 5^4 \times 2^3 \)). - Thus, \( -6 \sqrt[3]{5000} = -6 \times 10 \sqrt[3]{5} = -60 \sqrt[3]{5} \). - \( \sqrt[3]{40} = \sqrt[3]{2^3 \times 5} = 2 \sqrt[3]{5} \). - Therefore, \( 8 \sqrt[3]{40} = 8 \times 2 \sqrt[3]{5} = 16 \sqrt[3]{5} \). Combining these gives: \[ -60 \sqrt[3]{5} + 16 \sqrt[3]{5} = -44 \sqrt[3]{5}. \] 2. **Square Roots**: - \( \sqrt{20} = \sqrt{4 \times 5} = 2 \sqrt{5} \). - \( \sqrt{32} = \sqrt{16 \times 2} = 4 \sqrt{2} \). - Thus, \( -3 \sqrt{32} = -3 \times 4 \sqrt{2} = -12 \sqrt{2} \). Now, add the square root terms together. We have: \[ 2 \sqrt{5} - 12 \sqrt{2}. \] 3. **Final Expression**: Putting it all together, we get the simplified expression: \[ -44 \sqrt[3]{5} + 2 \sqrt{5} - 12 \sqrt{2}. \] So the final answer is: \[ -44 \sqrt[3]{5} + 2 \sqrt{5} - 12 \sqrt{2}. \]