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Multiply. Write your answer in simplest form. sqrt3(-8+sqrt5)

Multiply. Write your answer in simplest form.\newline3(−8+5) \sqrt{3}(-8+\sqrt{5})

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Simplify radical expressions using the distributive propertyright chevron icon

Full solution

Q. Multiply. Write your answer in simplest form.\newline3(−8+5) \sqrt{3}(-8+\sqrt{5})
  1. Distribute 3\sqrt{3}: Distribute 3\sqrt{3} to both terms inside the parentheses.\newline3(−8+5)=3×(−8)+3×5\sqrt{3}(-8 + \sqrt{5}) = \sqrt{3} \times (-8) + \sqrt{3} \times \sqrt{5}
  2. Multiply by −8-8: Multiply 3\sqrt{3} by −8-8.3×(−8)=−83\sqrt{3} \times (-8) = -8\sqrt{3}
  3. Multiply by 5\sqrt{5}: Multiply 3\sqrt{3} by 5\sqrt{5}.3×5=3×5=15\sqrt{3} \times \sqrt{5} = \sqrt{3\times5} = \sqrt{15}
  4. Combine the products: Combine the two products.\newline−83+15-8\sqrt{3} + \sqrt{15}

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