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Simplify. 8sqrt343

Simplify.\newline8343 8 \sqrt{343}

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Full solution

Q. Simplify.\newline8343 8 \sqrt{343}
  1. Identify Prime Factors: Identify the prime factors of 343343.\newline343=7×7×7343 = 7 \times 7 \times 7
  2. Rewrite with Prime Factors: Rewrite the square root with the prime factors. 8343=87×7×78\sqrt{343} = 8\sqrt{7 \times 7 \times 7}
  3. Group Identical Factors: Group the identical factors under the square root. 87×7×7=872×78\sqrt{7 \times 7 \times 7} = 8\sqrt{7^2 \times 7}
  4. Separate Perfect Square: Use the product property of radicals to separate the square root of the perfect square. \newline872×7=8×72×78\sqrt{7^2 \times 7} = 8 \times \sqrt{7^2} \times \sqrt{7}
  5. Simplify Perfect Square: Simplify the square root of the perfect square.\newline8×72×7=8×7×78 \times \sqrt{7^2} \times \sqrt{7} = 8 \times 7 \times \sqrt{7}
  6. Multiply Outside Numbers: Multiply the numbers outside the square root. 8×7×7=5678 \times 7 \times \sqrt{7} = 56\sqrt{7}

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