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Simplify. \newline3434\sqrt{\frac{343}{4}}

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Full solution

Q. Simplify. \newline3434\sqrt{\frac{343}{4}}
  1. Apply Quotient Rule: Apply the quotient rule of radicals to 3434\sqrt{\frac{343}{4}}.3434=3434\sqrt{\frac{343}{4}} = \frac{\sqrt{343}}{\sqrt{4}}
  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 4\sqrt{4}.\newline4=2×2\sqrt{4} = \sqrt{2 \times 2}\newline= 22
  4. Evaluate 4\sqrt{4}: Combine the results from the previous steps.\newline\sqrt{\frac{343}{4}} = \frac{\sqrt{343}}{\sqrt{4}}\(\newline= \frac{7 \times \sqrt{7}}{2}\)

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