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Simplify. \newline1254\sqrt{\frac{125}{4}}

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Full solution

Q. Simplify. \newline1254\sqrt{\frac{125}{4}}
  1. Apply Quotient Rule: Apply the quotient rule of radicals to 1254\sqrt{\frac{125}{4}}.1254=1254\sqrt{\frac{125}{4}} = \frac{\sqrt{125}}{\sqrt{4}}
  2. Evaluate 125\sqrt{125}: Evaluate 125\sqrt{125}. Find the prime factorization of 125125 and try to make identical pairs of factors. 125=5×5×5\sqrt{125} = \sqrt{5 \times 5 \times 5} = 5×55 \times \sqrt{5}
  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.1254=1254\sqrt{\frac{125}{4}} = \frac{\sqrt{125}}{\sqrt{4}} =5⋅52= \frac{5 \cdot \sqrt{5}}{2}

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