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Simplify.

2sqrt125

Simplify.\newline2125 2 \sqrt{125}

Full solution

Q. Simplify.\newline2125 2 \sqrt{125}
  1. Breakdown into Prime Factors: First, let's break down 125125 into its prime factors.\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. 2125=25×5×52\sqrt{125} = 2\sqrt{5 \times 5 \times 5}
  3. Pair Like Factors: We can pair the like factors under the square root. 25×5×5=252×52\sqrt{5 \times 5 \times 5} = 2\sqrt{5^2 \times 5}
  4. Take Square Root: Next, we can take the square root of the perfect square, which is 525^2. \newline252×5=2×5×52\sqrt{5^2 \times 5} = 2 \times 5 \times \sqrt{5}
  5. Multiply Outside Numbers: Finally, we multiply the numbers outside the square root. 2×5×5=1052 \times 5 \times \sqrt{5} = 10\sqrt{5}

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