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Multiply. Write your answer in simplest form.\newline330×3\sqrt{330}\times\sqrt{3}

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Full solution

Q. Multiply. Write your answer in simplest form.\newline330×3\sqrt{330}\times\sqrt{3}
  1. Find Prime Factorization: Find the prime factorization of 330330 and 33. The prime factorization of 330330 is 2×3×5×112 \times 3 \times 5 \times 11, and 33 is a prime number itself.
  2. Express Square Roots: Express 330×3\sqrt{330} \times \sqrt{3} as 2×3×5×11×3\sqrt{2 \times 3 \times 5 \times 11} \times \sqrt{3}.
  3. Apply Multiplication Property: Apply the multiplication property of square roots: 2×3×5×11×3=2×3×5×11×3\sqrt{2 \times 3 \times 5 \times 11} \times \sqrt{3} = \sqrt{2 \times 3 \times 5 \times 11 \times 3}.
  4. Simplify Expression: Simplify the expression: 2×3×5×11×3=2×32×5×11.\sqrt{2 \times 3 \times 5 \times 11 \times 3} = \sqrt{2 \times 3^2 \times 5 \times 11}.
  5. Pull Out Perfect Square Factor: Pull out the perfect square factor from the square root: 2×32×5×11=3×2×5×11\sqrt{2 \times 3^2 \times 5 \times 11} = 3 \times \sqrt{2 \times 5 \times 11}.
  6. Final Simplification: Simplify the expression: 3×2×5×11=3×110.3 \times \sqrt{2 \times 5 \times 11} = 3 \times \sqrt{110}.

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