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Multiply. Write your answer in simplest form. \newline5(8+3)\sqrt{5}(-8 + \sqrt{3})

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Q. Multiply. Write your answer in simplest form. \newline5(8+3)\sqrt{5}(-8 + \sqrt{3})
  1. Distribute 5\sqrt{5}: Distribute 5\sqrt{5} to both terms inside the parentheses.\newlineWe have the expression 5(8+3)\sqrt{5}(-8 + \sqrt{3}), which requires us to multiply 5\sqrt{5} with each term inside the parentheses separately.\newline5×(8)+5×3\sqrt{5} \times (-8) + \sqrt{5} \times \sqrt{3}
  2. Multiply by 8-8: Multiply 5\sqrt{5} by 8-8. When we multiply a square root by a real number, we simply multiply the number outside the radical with the real number. 5×(8)=8×5\sqrt{5} \times (-8) = -8 \times \sqrt{5}
  3. Multiply by 3\sqrt{3}: Multiply 5\sqrt{5} by 3\sqrt{3}.\newlineWhen we multiply two square roots together, we multiply the numbers inside the radicals.\newline5×3=5×3=15\sqrt{5} \times \sqrt{3} = \sqrt{5 \times 3} = \sqrt{15}
  4. Combine results: Combine the results from Step 22 and Step 33.\newlineWe have 8×5-8 \times \sqrt{5} from Step 22 and 15\sqrt{15} from Step 33. Combining these gives us the final simplified expression.\newline8×5+15-8 \times \sqrt{5} + \sqrt{15}

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