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Simplify. sqrt343

Simplify.\newline343 \sqrt{343}

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Full solution

Q. Simplify.\newline343 \sqrt{343}
  1. Find Prime Factors: Find the prime factors of 343343.343=7×49343 = 7 \times 49
  2. Recognize Perfect Square: Recognize that 4949 is a perfect square.\newline49=7×749 = 7 \times 7
  3. Write as Product of Primes: Write 343343 as a product of primes.\newline343=7×7×7343 = 7 \times 7 \times 7
  4. Group Identical Factors: Group the identical factors. 343=7×7×7\sqrt{343} = \sqrt{7 \times 7 \times 7}
  5. Use Product Property: Use the product property of radicals. 343=72×7\sqrt{343} = \sqrt{7^2 \times 7}
  6. Split Square Root: Split the square root into two parts. 343=72×7\sqrt{343} = \sqrt{7^2} \times \sqrt{7}
  7. Simplify Perfect Square: Simplify the square root of the perfect square. 343=7×7\sqrt{343} = 7 \times \sqrt{7}

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