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Simplify. \newline3439\sqrt{\frac{343}{9}}

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Full solution

Q. Simplify. \newline3439\sqrt{\frac{343}{9}}
  1. Apply Quotient Rule: Apply the quotient rule of radicals to 3439\sqrt{\frac{343}{9}}.3439=3439\sqrt{\frac{343}{9}} = \frac{\sqrt{343}}{\sqrt{9}}
  2. Evaluate 343\sqrt{343}: Evaluate 343\sqrt{343}.\newlineFind the prime factorization of 343343 and try to make identical pairs of factors.\newline343=7×7×7\sqrt{343} = \sqrt{7 \times 7 \times 7}\newline= 7×77 \times \sqrt{7}
  3. Find Prime Factorization: Now, let's evaluate 9\sqrt{9}.\newline9=3×3\sqrt{9} = \sqrt{3 \times 3}\newline= 33
  4. Evaluate 9\sqrt{9}: Combine the results from the previous steps.3439=3439\sqrt{\frac{343}{9}} = \frac{\sqrt{343}}{\sqrt{9}} =7⋅73= \frac{7 \cdot \sqrt{7}}{3}

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