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Simplify the expression 5 sqrt(75)

Check the final answer first, then review the worked steps.

Problem

Simplify the expression 5 * sqrt(75)

Answer

\(25\sqrt{3}\)

Step-by-step solution

  1. Identify the expression: The expression to simplify is $5\sqrt{75}$.
  2. Simplify the radical: We need to simplify $\sqrt{75}$. Find the largest perfect square factor of 75. The factors of 75 are 1, 3, 5, 15, 25, 75. The largest perfect square factor is 25.
  3. Rewrite the radical: Rewrite $\sqrt{75}$ as $\sqrt{25 \times 3}$.
  4. Separate the radicals: Using the property $\sqrt{ab} = \sqrt{a} \times \sqrt{b}$, we can write $\sqrt{25 \times 3}$ as $\sqrt{25} \times \sqrt{3}$.
  5. Calculate the square root of the perfect square: $\sqrt{25} = 5$.
  6. Substitute back into the expression: Now the expression becomes $5 \times (\sqrt{25} \times \sqrt{3}) = 5 \times (5 \times \sqrt{3})$.
  7. Multiply the coefficients: Multiply the numbers outside the radical: $5 \times 5 = 25$.
  8. Combine the terms: The simplified expression is $25\sqrt{3}$.