Simplify the radical.
$\(\sqrt{75}\)$

• A. $3\(\sqrt\)5$
• B. $3\(\sqrt{25}\)$
• C. $5\(\sqrt\)3$
• D. $25\(\sqrt\)3$

Answer: (C)

Verified step by step guidance

1. Identify the expression that needs simplification: \( 75\sqrt{75} \).
2. Break down \( \sqrt{75} \) into its prime factors: \( 75 = 3 \times 5^2 \).
3. Simplify \( \sqrt{75} \) by taking the square root of the perfect square factor: \( \sqrt{75} = \sqrt{3 \times 5^2} = 5\sqrt{3} \).
4. Multiply the simplified radical by the coefficient outside the radical: \( 75 \times 5\sqrt{3} = 375\sqrt{3} \).
5. Compare the simplified expression \( 375\sqrt{3} \) with the given options to determine the correct answer.