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Multiply. Write your answer in simplest form.\newline26⋅455\sqrt{26}\cdot\sqrt{455}

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Full solution

Q. Multiply. Write your answer in simplest form.\newline26⋅455\sqrt{26}\cdot\sqrt{455}
  1. Find Prime Factorization: Find the prime factorization of 26\sqrt{26} and 455\sqrt{455}. The prime factorization of 2626 is 2×132 \times 13, and the prime factorization of 455455 is 5×7×135 \times 7 \times 13.
  2. Combine Square Roots: Combine the square roots using the multiplication property: 26×455=26×455\sqrt{26} \times \sqrt{455} = \sqrt{26 \times 455}.
  3. Multiply Inside Square Root: Multiply the numbers inside the square root: 26×455=11830\sqrt{26 \times 455} = \sqrt{11830}.
  4. Factor to Find Perfect Squares: Factor 1183011830 to find perfect squares: 11830=2×5×7×13×1311830 = 2 \times 5 \times 7 \times 13 \times 13.
  5. Group Perfect Square Factors: Group the perfect square factors: 2×5×7×13×13=2×5×7×132\sqrt{2 \times 5 \times 7 \times 13 \times 13} = \sqrt{2 \times 5 \times 7 \times 13^2}.
  6. Pull Out Perfect Square Factor: Pull out the perfect square factor: 2×5×7×132=13×2×5×7\sqrt{2 \times 5 \times 7 \times 13^2} = 13 \times \sqrt{2 \times 5 \times 7}.
  7. Simplify the Expression: Simplify the expression: 13×2×5×7=13×70.13 \times \sqrt{2 \times 5 \times 7} = 13 \times \sqrt{70}.

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