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

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Full solution

Q. Multiply. Write your answer in simplest form. \newline5(−3−3)\sqrt{5}(-3 - \sqrt{3})
  1. Distribute 5\sqrt{5}: Distribute 5\sqrt{5} to both terms inside the parentheses.\newline5(−3−3)\sqrt{5}(-3 - \sqrt{3})\newline= 5×(−3)+5×(−3)\sqrt{5} \times (-3) + \sqrt{5} \times (-\sqrt{3})
  2. Multiply by −3-3: Now, multiply the square root of 55 by −3-3. 5×(−3)=−3×5\sqrt{5} \times (-3) = -3 \times \sqrt{5}
  3. Multiply by −3-\sqrt{3}: Next, multiply the square root of 55 by the negative square root of 33.5×(−3)=−5×3\sqrt{5} \times (-\sqrt{3}) = -\sqrt{5 \times 3}
  4. Simplify square roots: Simplify the product of the square roots.\newline−5×3=−15-\sqrt{5 \times 3} = -\sqrt{15}
  5. Combine products: Combine the two products to get the final answer.\newline−3×5−15-3 \times \sqrt{5} - \sqrt{15}

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