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Simplify. 10sqrt125

Simplify.\newline10125 10 \sqrt{125}

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Full solution

Q. Simplify.\newline10125 10 \sqrt{125}
  1. Find Prime Factors: First, let's find the prime factors of 125125.\newline125=5×25125 = 5 \times 25\newline125=5×5×5125 = 5 \times 5 \times 5
  2. Rewrite Using Prime Factors: Now, we can rewrite the square root of 125125 using its prime factors.\newline10125=105×5×510\sqrt{125} = 10\sqrt{5 \times 5 \times 5}
  3. Separate Square Roots: Next, we can use the product property of square roots to separate the square root of 55 squared from the square root of 55.105×5×5=1052×510\sqrt{5 \times 5 \times 5} = 10\sqrt{5^2} \times \sqrt{5}
  4. Simplify Square Root: Since the square root and the square cancel each other, we simplify 52\sqrt{5^2} to 55.\newline1052×5=10×5×510\sqrt{5^2} \times \sqrt{5} = 10 \times 5 \times \sqrt{5}
  5. Multiply and Simplify: Now, multiply 1010 by 55.10×5×5=50510 \times 5 \times \sqrt{5} = 50\sqrt{5}

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