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Multiply. Write your answer in simplest form. 3(−8+2)\sqrt{3}(-8 + \sqrt{2})

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Full solution

Q. Multiply. Write your answer in simplest form. 3(−8+2)\sqrt{3}(-8 + \sqrt{2})
  1. Distribute 3\sqrt{3}: Distribute 3\sqrt{3} to both terms inside the parentheses.\newline3(−8+2)\sqrt{3}(-8 + \sqrt{2})\newline= 3⋅(−8)+3⋅(2)\sqrt{3}\cdot(-8) + \sqrt{3}\cdot(\sqrt{2})
  2. Multiply by −8-8: Multiply 3\sqrt{3} by −8-8.3×(−8)=−8×3\sqrt{3} \times (-8) = -8 \times \sqrt{3}
  3. Multiply by 2\sqrt{2}: Multiply 3\sqrt{3} by 2\sqrt{2}.3×2\sqrt{3} \times \sqrt{2}Apply the product rule of radicals.=3×2= \sqrt{3 \times 2}=6= \sqrt{6}
  4. Combine results: Combine the results from Step 22 and Step 33.\newline−8×3+6-8 \times \sqrt{3} + \sqrt{6}\newlineThis is the simplest form since there are no like terms to combine.

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